Combinatorics and commutative algebra / Richard P. Stanley

Auteur: Stanley, Richard P. (1944-) - AuteurType de document: MonographieCollection: Progress in mathematics ; 41Langue: anglaisPays: Etats UnisÉditeur: Boston (Mass.) : Birkhäuser, 1983Description: 1 vol. (VIII-88 p.) ; 24 cm ISBN: 0817631127 ; rel. Résumé: 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 non-specialists. (Source : Springer).Bibliographie: Bibliogr. p. 86-88. Sujets MSC: 13C13 Commutative algebra -- Theory of modules and ideals -- Other special types
13H10 Commutative algebra -- Local rings and semilocal rings -- Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
52Bxx Convex and discrete geometry -- Polytopes and polyhedra
15-02 Linear and multilinear algebra; matrix theory -- Research exposition (monographs, survey articles)
52-02 Convex and discrete geometry -- Research exposition (monographs, survey articles)
11C20 Number theory -- Polynomials and matrices -- Matrices, determinants
En-ligne: Springerlink - ed. 1996
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Bibliogr. p. 86-88

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 non-specialists. (Source : Springer)

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