Combinatorial Reciprocity Theorems : An Invitation to Enumerative Geometric Combinatorics (Graduate Studies in Mathematics)

Beck, Matthias/ Sanyal, Raman

American Mathematical Society（2019/02発売）

• 製本 Hardcover:ハードカバー版／ページ数 314 p.
• 言語 ENG
• 商品コード 9781470422004
• DDC分類 511.6

Full Description

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.

Contents

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