Stanley, Richard P. 1944
Overview
Works:  49 works in 361 publications in 5 languages and 5,582 library holdings 

Genres:  Textbooks Conference papers and proceedings 
Roles:  Author, Editor, Author of introduction 
Classifications:  QA164, 511.62 
Publication Timeline
.
Most widely held works about
Richard P Stanley
 The mathematical legacy of Richard P. Stanley( Book )
 Selected works of Richard P. Stanley by Richard P Stanley( Book )
Most widely held works by
Richard P Stanley
Enumerative combinatorics by
Richard P Stanley(
Book
)
97 editions published between 1900 and 2012 in 3 languages and held by 1,267 WorldCat member libraries worldwide
Publisher Description (unedited publisher data) This second volume of a twovolume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, Dfinite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important RobinsonSchenstedKnuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the LittlewoodRichardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference. Library of Congress subject headings for this publication: Combinatorial enumeration problems
97 editions published between 1900 and 2012 in 3 languages and held by 1,267 WorldCat member libraries worldwide
Publisher Description (unedited publisher data) This second volume of a twovolume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, Dfinite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important RobinsonSchenstedKnuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the LittlewoodRichardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference. Library of Congress subject headings for this publication: Combinatorial enumeration problems
Enumerative combinatorics by
Richard P Stanley(
)
31 editions published between 1999 and 2010 in English and held by 1,097 WorldCat member libraries worldwide
This second volume of a twovolume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, Dfinite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important RobinsonSchenstedKnuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the LittlewoodRichardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference
31 editions published between 1999 and 2010 in English and held by 1,097 WorldCat member libraries worldwide
This second volume of a twovolume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, Dfinite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important RobinsonSchenstedKnuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the LittlewoodRichardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference
Combinatorics and commutative algebra by
Richard P Stanley(
Book
)
21 editions published between 1983 and 2005 in English and German and held by 825 WorldCat member libraries worldwide
Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for nonspecialists. New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to fvectors. Included in this chapter is an outline of the proof of McMullen's gconjecture for simplicial polytopes based on toric varieties, as well as a discussion of the face rings of such special classes of simplicial complexes as shellable complexes, matroid complexes, level complexes, doubly CohenMacaulay complexes, balanced complexes, order complexes, flag complexes, relative complexes, and complexes with group actions. Also included is information on subcomplexes and subdivisions of simplicial complexes, and an application to spline theory
21 editions published between 1983 and 2005 in English and German and held by 825 WorldCat member libraries worldwide
Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for nonspecialists. New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to fvectors. Included in this chapter is an outline of the proof of McMullen's gconjecture for simplicial polytopes based on toric varieties, as well as a discussion of the face rings of such special classes of simplicial complexes as shellable complexes, matroid complexes, level complexes, doubly CohenMacaulay complexes, balanced complexes, order complexes, flag complexes, relative complexes, and complexes with group actions. Also included is information on subcomplexes and subdivisions of simplicial complexes, and an application to spline theory
Algebraic combinatorics : walks, trees, tableaux, and more by
Richard P Stanley(
)
26 editions published between 2013 and 2018 in English and held by 661 WorldCat member libraries worldwide
(Unedited publisher data) Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author's extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a onesemester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the MatrixTree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser
26 editions published between 2013 and 2018 in English and held by 661 WorldCat member libraries worldwide
(Unedited publisher data) Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author's extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a onesemester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the MatrixTree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser
Enumerative combinatorics by
Richard P Stanley(
Book
)
23 editions published between 1986 and 2012 in English and held by 337 WorldCat member libraries worldwide
"Richard Stanley's twovolume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on Ppartitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on qanalogues of permutations, hyperplane arrangements, the cdindex, promotion and evacuation and differential posets"
23 editions published between 1986 and 2012 in English and held by 337 WorldCat member libraries worldwide
"Richard Stanley's twovolume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on Ppartitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on qanalogues of permutations, hyperplane arrangements, the cdindex, promotion and evacuation and differential posets"
Mathematical essays in honor of GianCarlo Rota by
Bruce Eli Sagan(
Book
)
16 editions published between 1996 and 1998 in English and held by 330 WorldCat member libraries worldwide
The Mathematical Essays in this volume pay tribute to GianCarlo Rota in honor of his 64th birthday. The breadth and depth of Rota's interests, research, and influence are reflected in such areas as combinatorics, invariant theory, geometry, algebraic topology, representation theory, and umbral calculus, one paper coauthored by Rota himself on the umbral calculus. Other important areas of research that are touched on in this collection include special functions, commutative algebra, and statistics
16 editions published between 1996 and 1998 in English and held by 330 WorldCat member libraries worldwide
The Mathematical Essays in this volume pay tribute to GianCarlo Rota in honor of his 64th birthday. The breadth and depth of Rota's interests, research, and influence are reflected in such areas as combinatorics, invariant theory, geometry, algebraic topology, representation theory, and umbral calculus, one paper coauthored by Rota himself on the umbral calculus. Other important areas of research that are touched on in this collection include special functions, commutative algebra, and statistics
Ordered structures and partitions by
Richard P Stanley(
Book
)
20 editions published between 1971 and 2012 in 3 languages and held by 271 WorldCat member libraries worldwide
"A general theory is developed for the enumeration of order reversing maps of finite ordered sets [italic]P into chains. This theory encompasses many apparently disparate topics in combinatorial theory, including (1) ordinary partitions, (2) ordered partitions (compositions), (3) plane and multidimensional partitions, with applications to Young tableaux, (4) the Eulerian numbers and their refinements, (5) the tangent and secant numbers (or Euler numbers) and their refinements, (6) the indices of permutations, (7) trees, (8) stacks, and (9) protruded partitions, with applications to the Fibonacci numbers. The main tool used is that of generating functions. In particular, we study how the structure of [italic]P influences the form of the generating functions under consideration. As an application, we derive new combinatorial relationships between a finite ordered set [italic]P and its distributive lattice of order ideals."Abstract
20 editions published between 1971 and 2012 in 3 languages and held by 271 WorldCat member libraries worldwide
"A general theory is developed for the enumeration of order reversing maps of finite ordered sets [italic]P into chains. This theory encompasses many apparently disparate topics in combinatorial theory, including (1) ordinary partitions, (2) ordered partitions (compositions), (3) plane and multidimensional partitions, with applications to Young tableaux, (4) the Eulerian numbers and their refinements, (5) the tangent and secant numbers (or Euler numbers) and their refinements, (6) the indices of permutations, (7) trees, (8) stacks, and (9) protruded partitions, with applications to the Fibonacci numbers. The main tool used is that of generating functions. In particular, we study how the structure of [italic]P influences the form of the generating functions under consideration. As an application, we derive new combinatorial relationships between a finite ordered set [italic]P and its distributive lattice of order ideals."Abstract
Catalan numbers by
Richard P Stanley(
Book
)
11 editions published in 2015 in English and held by 180 WorldCat member libraries worldwide
Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. Following an introduction to the basic properties of Catalan numbers, the book presents 214 different kinds of objects counted by them in the form of exercises with solutions. The reader can try solving the exercises or simply browse through them. Some 68 additional exercises with prescribed difficulty levels present various properties of Catalan numbers and related numbers, such as FussCatalan numbers, Motzkin numbers, Schröder numbers, Narayana numbers, super Catalan numbers, qCatalan numbers and (q, t)Catalan numbers. The book ends with a history of Catalan numbers by Igor Pak and a glossary of key terms. Whether your interest in mathematics is recreation or research, you will find plenty of fascinating and stimulating facts here
11 editions published in 2015 in English and held by 180 WorldCat member libraries worldwide
Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. Following an introduction to the basic properties of Catalan numbers, the book presents 214 different kinds of objects counted by them in the form of exercises with solutions. The reader can try solving the exercises or simply browse through them. Some 68 additional exercises with prescribed difficulty levels present various properties of Catalan numbers and related numbers, such as FussCatalan numbers, Motzkin numbers, Schröder numbers, Narayana numbers, super Catalan numbers, qCatalan numbers and (q, t)Catalan numbers. The book ends with a history of Catalan numbers by Igor Pak and a glossary of key terms. Whether your interest in mathematics is recreation or research, you will find plenty of fascinating and stimulating facts here
Combinatorics and commutative algebra by
Richard P Stanley(
Book
)
17 editions published between 1983 and 2004 in English and French and held by 89 WorldCat member libraries worldwide
Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for nonspecialists. New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to fvectors. Included in this chapter is an outline of the proof of McMullen's gconjecture for simplicial polytopes based on toric varieties, as well as a discussion of the face rings of such special classes of simplicial complexes as shellable complexes, matroid complexes, level complexes, doubly CohenMacaulay complexes, balanced complexes, order complexes, flag complexes, relative complexes, and complexes with group actions. Also included is information on subcomplexes and subdivisions of simplicial complexes, and an application to spline theory
17 editions published between 1983 and 2004 in English and French and held by 89 WorldCat member libraries worldwide
Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for nonspecialists. New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to fvectors. Included in this chapter is an outline of the proof of McMullen's gconjecture for simplicial polytopes based on toric varieties, as well as a discussion of the face rings of such special classes of simplicial complexes as shellable complexes, matroid complexes, level complexes, doubly CohenMacaulay complexes, balanced complexes, order complexes, flag complexes, relative complexes, and complexes with group actions. Also included is information on subcomplexes and subdivisions of simplicial complexes, and an application to spline theory
Enumerative combinatorics by
Richard P Stanley(
Book
)
13 editions published between 1986 and 2008 in English and Undetermined and held by 79 WorldCat member libraries worldwide
13 editions published between 1986 and 2008 in English and Undetermined and held by 79 WorldCat member libraries worldwide
A combinatorial miscellany by
Anders Björner(
Book
)
7 editions published in 2010 in English and French and held by 56 WorldCat member libraries worldwide
7 editions published in 2010 in English and French and held by 56 WorldCat member libraries worldwide
Enumerative combinatorics by
Richard P Stanley(
Book
)
9 editions published between 1999 and 2010 in English and Undetermined and held by 50 WorldCat member libraries worldwide
9 editions published between 1999 and 2010 in English and Undetermined and held by 50 WorldCat member libraries worldwide
Current Developments in Mathematics 2013(
Book
)
1 edition published in 2014 in English and held by 18 WorldCat member libraries worldwide
1 edition published in 2014 in English and held by 18 WorldCat member libraries worldwide
A walk through combinatorics : an introduction to enumeration and graph theory by
Miklós Bóna(
Book
)
8 editions published between 2002 and 2017 in English and held by 15 WorldCat member libraries worldwide
Textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first edition, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible for the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity. every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading
8 editions published between 2002 and 2017 in English and held by 15 WorldCat member libraries worldwide
Textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first edition, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible for the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity. every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading
Enumerative combinatorics, v.2 by
Richard P Stanley(
)
1 edition published in 1999 in English and held by 15 WorldCat member libraries worldwide
1 edition published in 1999 in English and held by 15 WorldCat member libraries worldwide
Combinatorics and commutative algebra by
Richard P Stanley(
Book
)
4 editions published between 1983 and 1996 in English and held by 13 WorldCat member libraries worldwide
4 editions published between 1983 and 1996 in English and held by 13 WorldCat member libraries worldwide
Current developments in mathematics 2012(
Book
)
1 edition published in 2013 in English and held by 12 WorldCat member libraries worldwide
1 edition published in 2013 in English and held by 12 WorldCat member libraries worldwide
Current developments in mathematics 2015(
Book
)
3 editions published in 2016 in English and held by 12 WorldCat member libraries worldwide
3 editions published in 2016 in English and held by 12 WorldCat member libraries worldwide
Catalan numbers by
Richard P Stanley(
)
1 edition published in 2015 in English and held by 9 WorldCat member libraries worldwide
1 edition published in 2015 in English and held by 9 WorldCat member libraries worldwide
Current developments in mathematics 2016(
Book
)
2 editions published in 2018 in English and held by 9 WorldCat member libraries worldwide
2 editions published in 2018 in English and held by 9 WorldCat member libraries worldwide
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Related Identities
 Sagan, Bruce Eli Author Editor
 Rota, GianCarlo 19321999 Honoree
 Hersh, Patricia 1973 Editor
 Lam, Thomas 1980 Editor
 Reiner, Victor 1965 Editor
 Pylyavskyy, Pavlo 1982 Editor
 Björner, Anders Author Editor
 Yau, HorngTzer Editor
 Jerison, David 1953 Editor
 Kisin, Mark 1971 Editor
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Alternative Names
Ričard P. Stenli
Richard P. Stanley Amerikaans wiskundige
Richard P. Stanley amerikansk matematikar
Richard P. Stanley amerikansk matematiker
Richard P. Stanley matemático estadounidense
Richard P. Stanley matematico statunitense
Richard P. Stanley USamerikanischer Mathematiker
Richard Peter Stanley mathématicien américain
Richard Stanley matematico statunitense
Stanley, R. 1944
Stanley, R. P
Stanley, R. P. 1944
Stanley, Richard
Stanley, Richard 1944
Stanley, Richard P.
Stanley, Richard Peter
Stanley, Richard Peter 1944
Ричард П. Стенли
Стенли, Р 1944
ریچارد استنلی
ریچارد پی. استنلی ریاضیدان آمریکایی
スタンレイ, リチャード
理查德·P·斯坦利
Languages