Combinatorics and Commutative Algebra
Birkhauser Boston Inc (Verlag)
978-0-8176-3836-8 (ISBN)
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* Stanley represents a broad perspective with respect to two significant topics from Combinatorial Commutative Algebra: 1) The theory of invariants of a torus acting linearly on a polynomial ring, and 2) The face ring of a simplicial complex * In this new edition, the author further develops some interesting properties of face rings with application to combinatorics
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.
| Reihe/Serie | Progress in Mathematics ; 41 |
|---|---|
| Zusatzinfo | biography |
| Verlagsort | Secaucus |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 460 g |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| ISBN-10 | 0-8176-3836-9 / 0817638369 |
| ISBN-13 | 978-0-8176-3836-8 / 9780817638368 |
| Zustand | Neuware |
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