Klee, Victor
Overview
Works:  138 works in 324 publications in 2 languages and 2,897 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Translator, Honoree, Contributor, Other, Dedicatee, Creator 
Publication Timeline
.
Most widely held works by
Victor Klee
Old and new unsolved problems in plane geometry and number theory by
Victor Klee(
Book
)
20 editions published between 1991 and 1996 in English and held by 877 WorldCat member libraries worldwide
Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the
20 editions published between 1991 and 1996 in English and held by 877 WorldCat member libraries worldwide
Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the
Convexity : proceedings of the Seventh Symposium in Pure Mathematics of the American Mathematical Society : held at the University
of Washington, Seattle, Washington, June 1315, 1961 by Symposium on Convexity(
Book
)
35 editions published between 1963 and 1972 in English and Undetermined and held by 513 WorldCat member libraries worldwide
35 editions published between 1963 and 1972 in English and Undetermined and held by 513 WorldCat member libraries worldwide
Convex polytopes by
Branko Grünbaum(
Book
)
9 editions published in 2003 in English and held by 362 WorldCat member libraries worldwide
"The appearance of Grünbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way." (Gil Kalai, The Hebrew University of Jerusalem) "The original book of Grünbaum has provided the central reference for work in this active area of mathematics for the past 35 years ... I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day." (Louis J. Billera, Cornell University) "The original edition of Convex Polytopes inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." (Peter McMullen, University College London)
9 editions published in 2003 in English and held by 362 WorldCat member libraries worldwide
"The appearance of Grünbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way." (Gil Kalai, The Hebrew University of Jerusalem) "The original book of Grünbaum has provided the central reference for work in this active area of mathematics for the past 35 years ... I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day." (Louis J. Billera, Cornell University) "The original edition of Convex Polytopes inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." (Peter McMullen, University College London)
Combinatorial and graphtheoretical problems in linear algebra by
Richard A Brualdi(
Book
)
10 editions published in 1993 in English and held by 267 WorldCat member libraries worldwide
This volume aims to gather information from both those who work on linear algebra problems in which combinatorial or graphtheoretical analysis is a major component and those that work on combinatorial or graphtheoretical problems for which linear algebra is a major tool. The fifteen papers in this volume span a wide crosssection of past and current research in the field. Specific topics covered in the papers include matrix problems and results in symbolic dynamics, blocktriangular decompositions of mixed matrices, algebraic and geometric properties of Laplacian matrices of graphs, the use of eigenvalues in combinatorial optimization, perturbation effects on rank and eigenvalues, and polynomial spaces. This book should be of interest to researchers in linear algebra, combinatorics and graph theory, and to anyone who wishes to get a glimpse of this fascinating area
10 editions published in 1993 in English and held by 267 WorldCat member libraries worldwide
This volume aims to gather information from both those who work on linear algebra problems in which combinatorial or graphtheoretical analysis is a major component and those that work on combinatorial or graphtheoretical problems for which linear algebra is a major tool. The fifteen papers in this volume span a wide crosssection of past and current research in the field. Specific topics covered in the papers include matrix problems and results in symbolic dynamics, blocktriangular decompositions of mixed matrices, algebraic and geometric properties of Laplacian matrices of graphs, the use of eigenvalues in combinatorial optimization, perturbation effects on rank and eigenvalues, and polynomial spaces. This book should be of interest to researchers in linear algebra, combinatorics and graph theory, and to anyone who wishes to get a glimpse of this fascinating area
Applied geometry and discrete mathematics : the Victor Klee festschrift(
Book
)
9 editions published in 1991 in English and held by 171 WorldCat member libraries worldwide
9 editions published in 1991 in English and held by 171 WorldCat member libraries worldwide
Combinatorial geometry in the plane by
Hugo Hadwiger(
)
10 editions published between 1964 and 2015 in English and German and held by 103 WorldCat member libraries worldwide
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research. The twopart treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second part consists of an extensive section of short proofs concerning the earlier material
10 editions published between 1964 and 2015 in English and German and held by 103 WorldCat member libraries worldwide
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research. The twopart treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second part consists of an extensive section of short proofs concerning the earlier material
Alte und neue ungelöste Probleme in der Zahlentheorie und Geometrie der Ebene by
Victor Klee(
Book
)
5 editions published between 1997 and 2015 in German and held by 63 WorldCat member libraries worldwide
5 editions published between 1997 and 2015 in German and held by 63 WorldCat member libraries worldwide
Convex polytopes by
Branko Grünbaum(
Book
)
10 editions published between 1967 and 2000 in English and held by 46 WorldCat member libraries worldwide
"The original edition ... inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again."Peter McMullen, University College London
10 editions published between 1967 and 2000 in English and held by 46 WorldCat member libraries worldwide
"The original edition ... inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again."Peter McMullen, University College London
Combinatorial Geometry in the Plane by
Victor Klee(
)
1 edition published in 2014 in English and held by 30 WorldCat member libraries worldwide
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research. The twopart treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second part consists of an extensive section of short proofs concerning the earlier material
1 edition published in 2014 in English and held by 30 WorldCat member libraries worldwide
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research. The twopart treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second part consists of an extensive section of short proofs concerning the earlier material
Computational complexity of inner and outer jRADII of polytopes in finite dimensional normed spaces by
Peter Gritzmann(
Book
)
7 editions published between 1990 and 1993 in English and German and held by 23 WorldCat member libraries worldwide
7 editions published between 1990 and 1993 in English and German and held by 23 WorldCat member libraries worldwide
Polytope containment and determination by linear probes by
Peter Gritzmann(
Book
)
5 editions published in 1992 in English and German and held by 22 WorldCat member libraries worldwide
5 editions published in 1992 in English and German and held by 22 WorldCat member libraries worldwide
Largest jsimplices in npolytopes by
Peter Gritzmann(
Book
)
5 editions published between 1993 and 1994 in English and German and held by 21 WorldCat member libraries worldwide
5 editions published between 1993 and 1994 in English and German and held by 21 WorldCat member libraries worldwide
Polytope projection and projection polytopes by
Thomas Burger(
Book
)
2 editions published in 1995 in English and held by 21 WorldCat member libraries worldwide
2 editions published in 1995 in English and held by 21 WorldCat member libraries worldwide
Crosspositive matrices revisited by
Peter Gritzmann(
Book
)
6 editions published between 1992 and 1993 in English and German and held by 20 WorldCat member libraries worldwide
6 editions published between 1992 and 1993 in English and German and held by 20 WorldCat member libraries worldwide
Maximal separation theorems for convex sets by
Victor Klee(
Book
)
2 editions published in 1967 in English and held by 19 WorldCat member libraries worldwide
Most previous applications of separation theorems for convex sets have depended on rather crude separation results. Recent developments, however, indicate a need for more refined theorems, particularly for ones involving stronger types of separation. The stronger types of separation considered in this study include nice, open, closed, strict, and strong. The attempt to obtain separation theorems under minimal hypotheses suggests a search for maximal theorems, since each such theorem is, in a sense, a best possible result. Eighteen maximal theorems for disjoint nonempty convex subsets are derived, involving open, nice, strong and strict separation. (Author)
2 editions published in 1967 in English and held by 19 WorldCat member libraries worldwide
Most previous applications of separation theorems for convex sets have depended on rather crude separation results. Recent developments, however, indicate a need for more refined theorems, particularly for ones involving stronger types of separation. The stronger types of separation considered in this study include nice, open, closed, strict, and strong. The attempt to obtain separation theorems under minimal hypotheses suggests a search for maximal theorems, since each such theorem is, in a sense, a best possible result. Eighteen maximal theorems for disjoint nonempty convex subsets are derived, involving open, nice, strong and strict separation. (Author)
Invertibly positive linear operators on spaces of continuous functions by
Thomas A Brown(
Book
)
3 editions published in 1968 in English and held by 19 WorldCat member libraries worldwide
A proof is given that any positive linear transformation of a space of continuous functions with a positive inverse has a certain specific form. The characterization is the same as that found by Kaplansky and others, but here it is obtained under weaker assumptions as to the topological space X and the linear space F of realvalued functions. The study was motivated by a problem in logistics, which, mathematically, was to find conditions necessary and sufficient for a positive matrix to have one of its powers equal to the identity matrix. (Author)
3 editions published in 1968 in English and held by 19 WorldCat member libraries worldwide
A proof is given that any positive linear transformation of a space of continuous functions with a positive inverse has a certain specific form. The characterization is the same as that found by Kaplansky and others, but here it is obtained under weaker assumptions as to the topological space X and the linear space F of realvalued functions. The study was motivated by a problem in logistics, which, mathematically, was to find conditions necessary and sufficient for a positive matrix to have one of its powers equal to the identity matrix. (Author)
Separation by hyperplanes in finite dimensional vector spaces over Archimedean ordered fields by
Peter Gritzmann(
Book
)
3 editions published in 1997 in English and held by 18 WorldCat member libraries worldwide
3 editions published in 1997 in English and held by 18 WorldCat member libraries worldwide
External tangents and closedness of cone + subspace by
Peter Gritzmann(
Book
)
5 editions published between 1992 and 1993 in English and German and held by 18 WorldCat member libraries worldwide
5 editions published between 1992 and 1993 in English and German and held by 18 WorldCat member libraries worldwide
Geometry of the GassSaaty parametric cost LP algorithm by
Victor Klee(
Book
)
4 editions published in 1987 in English and held by 14 WorldCat member libraries worldwide
4 editions published in 1987 in English and held by 14 WorldCat member libraries worldwide
A method for constructing circuit codes by
Victor Klee(
Book
)
2 editions published in 1966 in English and held by 14 WorldCat member libraries worldwide
A ddimensional circuit code of spread s is a simple circuit Q in the graph of the ddimensional cube (0, 1)d such that any two vertices of Q differing in exactly r coordinates, with r <s, can be joined by a path formed from r edges of Q. Such codes are designed to introduce error detection into certain analogtodigital conversion systems. Longer codes correspond to increased accuracy in determining the maxmum length C(d, s) of ddimensional circuit codes of spread s. This study contributes to the problem for even values of s by describing a method for combining a code of spread s with a suitably related code of spread s  1 so as to produce a longer code of spread s. (Author)
2 editions published in 1966 in English and held by 14 WorldCat member libraries worldwide
A ddimensional circuit code of spread s is a simple circuit Q in the graph of the ddimensional cube (0, 1)d such that any two vertices of Q differing in exactly r coordinates, with r <s, can be joined by a path formed from r edges of Q. Such codes are designed to introduce error detection into certain analogtodigital conversion systems. Longer codes correspond to increased accuracy in determining the maxmum length C(d, s) of ddimensional circuit codes of spread s. This study contributes to the problem for even values of s by describing a method for combining a code of spread s with a suitably related code of spread s  1 so as to produce a longer code of spread s. (Author)
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Related Identities
 Wagon, S. Author
 American Mathematical Society Editor
 Grünbaum, Branko Honoree Author
 University of Washington
 Gritzmann, Peter 1954 Author Editor
 Ziegler, Günter M. Editor
 Kaibel, Volker Editor
 Brualdi, Richard A. Author Editor
 Friedland, Shmuel Editor
 Sturmfels, Bernd 1962 Editor
Useful Links
Associated Subjects
Algebras, Linear Combinatorial analysis Combinatorial geometry Computational complexity ComputersCircuits Cone Cones (Operator theory) Convex bodies Convex domains Convex functions Convex geometry Convex polytopes Convex sets Discrete groups Electronic circuit design Functions, Continuous Geometry, Plane GeometryFamous problems Graph theory Klee, Victor Mathematics Matrices Normed linear spaces Number theory Ordered fields Orthographic projection Polytopes Probes (Electronic instruments) Projection Set theory Simplexes (Mathematics) Transformations (Mathematics) Vector lattices, Archimedian Vector spaces
Covers
Alternative Names
Klee, V. 1925
Klee, V. 19252007
Klee, V. L. 19252007
Klee, V. L. (Victor L.)
Klee, Victor E. 1925
Klee, Victor L.
Klee, Victor L. 1925
Klee, Victor L. 19252007
Klee Victor La Rue
Klee, Victor LaRue 19252007
Klee, Viktor 19252007
Kli, V.
Kli, V. 19252007
La Rue Klee Victor
Victor Klee Amerikaans wiskundige (19252007)
Victor Klee amerikansk matematikar
Victor Klee amerikansk matematiker
Victor Klee matematico statunitense
Victor Klee mathématicien américain
Victor Klee USamerikanischer Mathematiker
Виктор Кли
Кли, В..
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