Combinatorial Reciprocity Theorems: An Invitation to Enumerative Geometric Combinatorics

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Matthias Beck Raman Sanyal

Combinatorial Reciprocity Theorems

Name: Combinatorial Reciprocity Theorems
Price: 312 AUD
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ISBN: 9781470422004

An Invitation to Enumerative Geometric Combinatorics

Matthias Beck, Raman Sanyal

$312

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English

American Mathematical Society
28 February 2019

Discrete mathematics; Combinatorics & graph theory

Series: Graduate Studies in Mathematics

Combinatorial reciprocity is a very interesting phenomenon, which can be described as follows: A polynomial, whose values at positive integers count combinatorial objects of some sort, may give the number of combinatorial objects of a different sort when evaluated at negative integers (and suitably normalized). Such combinatorial reciprocity theorems occur in connections with graphs, partially ordered sets, polyhedra, and more. Using the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics.

Written in a friendly writing style, this is an accessible graduate textbook with almost 300 exercises, numerous illustrations, and pointers to the research literature. Topics include concise introductions to partially ordered sets, polyhedral geometry, and rational generating functions, followed by highly original chapters on subdivisions, geometric realizations of partially ordered sets, and hyperplane arrangements.

By: Matthias Beck, Raman Sanyal
Imprint: American Mathematical Society
Country of Publication: United States
Dimensions: Height: 254mm, Width: 178mm,
Weight: 708g
ISBN: 9781470422004
ISBN 10: 147042200X
Series: Graduate Studies in Mathematics
Pages: 314
Publication Date: 28 February 2019
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Four polynomials Partially ordered sets Polyhedral geometry Rational generating functions Subdivisions Partially ordered sets, geometrically Hyperplane arrangements Bibliography Notation index Index.

Matthias Beck, San Francisco State University, CA. Raman Sanyal, Goethe-Universitat Frankfurt, Germany.