Combinatorics and Commutative Algebra

Richard P. Stanley

ISBN 10: 0817643699 / ISBN 13: 9780817643690

Editore: Birkhäuser Boston, Birkhäuser Boston Okt 2004, 2004

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Neuware -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.New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to f-vectors.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 180 pp. Englisch.

Codice articolo 9780817643690

Dati bibliografici

• Titolo: Combinatorics and Commutative Algebra
• Editore: Birkhäuser Boston, Birkhäuser Boston Okt 2004
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 0817643699
• ISBN 13: 9780817643690
• Rilegatura: Taschenbuch
• Edizione: seconda edizione
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 11 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 11 millimetri di profondità
• Peso: 283 grammi

Descrizione articolo

Riassunto

An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for non-specialists.

New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to f-vectors.

Dalla quarta di copertina

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.

New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to f-vectors. Included in this chapter is an outline of the proof of McMullen's g-conjecture 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 Cohen-Macaulay 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.