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Combinatorics and commutative algebra

Author: Richard P Stanley
Publisher: Boston [Mass.] : Birkhäuser, ©1996.
Series: Progress in mathematics, 41.
Edition/Format:   eBook : Document : English : 2nd edView all editions and formats
Summary:

Contains a significant amount of new in areas of interest, and presents the "big picture" in an engaging framework.

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Genre/Form: Llibres electrònics
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Richard P Stanley
OCLC Number: 805065750
Notes: Descripció del recurs: 18 abril 2011.
Description: 1 online resource (1 recurs electrònic (VI, 164 p.)) : il
Contents: Contents.- Preface to the Second Edition.- Preface to the First Edition.- Notation.- Background: Combinatorics.- Commutative algebra and homological algebra.- Topology.- Chapter I: Nonnegative Integral Solutions to Linear Equations: Integer stochastic matrices (magic squares).- Graded algebras and modules.- Elementary aspects of N-solutions to linear equations.- Integer stochastic matrices again.- Dimension, depth, and Cohen-Macaulay modules.- Local cohomology.- Local cohomology of the modules M phi,alpha.- Reciprocity.- Reciprocity for integer stochastic matrices.- Rational points in integer polytopes.- Free resolutions.- Duality and canonical modules.- A final look at linear equations.- Chapter II: The Face Ring of a Simplicial Complex: Elementary properties of the face ring.- f-vectors and h-vectors of complexes and multicomplexes.- Cohen-Macaulay complexes and the Upper Bound Conjecture.- Homological properties of face rings.- Gorenstein face rings.- Gorenstein Hilbert Functions.- Canonical modules of face rings.- Buchsbaum complexes.- Chapter III: Further Aspects of Face Rings: Simplicial polytopes, toric varieties, and the g-theorem.- Shellable simplicial complexes.- Matroid complexes, level complexes, and doubly Cohen-Macaulay complexes.- Balances complexes, order complexes, and flag complexes.- Splines.- Algebras with straightening law and simplical posets.- Relative simplical complexes.- Group actions.- Subcomplexes.- Subdivisions.- Problems on Simplicial Complexes and their Face Rings.- Bibliography.- Index.
Series Title: Progress in mathematics, 41.
Responsibility: Richard P. Stanley.

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