[PDF] Combinatorial Reciprocity Theorems An Invitation To Enumerative Geometric Combinatorics eBook

Author : Matthias Beck
Publisher : American Mathematical Soc.
Page : 308 pages
File Size : 31,17 MB
Release : 2018-12-12
Category : Combinatorial analysis
ISBN : 147042200X

GET BOOK

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.

Author : Christos A. Athanasiadis
Publisher : American Mathematical Soc.
Page : 342 pages
File Size : 24,15 MB
Release : 2006
Category : Mathematics
ISBN : 0821840800

GET BOOK

This volume contains original research and survey articles stemming from the Euroconference ``Algebraic and Geometric Combinatorics''. The papers discuss a wide range of problems that illustrate interactions of combinatorics with other branches of mathematics, such as commutative algebra, algebraic geometry, convex and discrete geometry, enumerative geometry, and topology of complexes and partially ordered sets. Among the topics covered are combinatorics of polytopes, lattice polytopes, triangulations and subdivisions, Cohen-Macaulay cell complexes, monomial ideals, geometry of toric surfaces, groupoids in combinatorics, Kazhdan-Lusztig combinatorics, and graph colorings. This book is aimed at researchers and graduate students interested in various aspects of modern combinatorial theories.

Author : Ezra Miller
Publisher : American Mathematical Soc.
Page : 705 pages
File Size : 22,34 MB
Release : 2007
Category : Combinatorial analysis
ISBN : 0821837362

GET BOOK

Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.

Author : Rekha R. Thomas
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 42,69 MB
Release : 2006
Category : Mathematics
ISBN : 9780821841402

GET BOOK

This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the statepolytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Grobner bases of toric ideals and other methods fromcommutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.

Author : Hibi Takayuki
Publisher : World Scientific
Page : 476 pages
File Size : 31,57 MB
Release : 2019-05-30
Category : Mathematics
ISBN : 9811200491

GET BOOK

This volume consists of research papers and expository survey articles presented by the invited speakers of the Summer Workshop on Lattice Polytopes. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further developments of many research areas surrounding this field. With the survey articles, research papers and open problems, this volume provides its fundamental materials for graduate students to learn and researchers to find exciting activities and avenues for further exploration on lattice polytopes.

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
Page : 304 pages
File Size : 48,79 MB
Release : 2020-10-16
Category : Education
ISBN : 1470460327

GET BOOK

This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Author : E. Mendelsohn
Publisher : Elsevier
Page : 393 pages
File Size : 42,99 MB
Release : 1982-01-01
Category : Mathematics
ISBN : 0080871763

GET BOOK

Algebraic and Geometric Combinatorics

Author : Miklos Bona
Publisher : CRC Press
Page : 1073 pages
File Size : 12,81 MB
Release : 2015-03-24
Category : Mathematics
ISBN : 1482220865

GET BOOK

Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.This important new work is edited by Miklos Bona of the University of Florida where he