Using the Borsuk Ulam Theorem

Author: Jiri Matousek
Publisher: Springer Science & Business Media
ISBN: 9783540766490
Release Date: 2008-01-12
Genre: Mathematics

To the uninitiated, algebraic topology might seem fiendishly complex, but its utility is beyond doubt. This brilliant exposition goes back to basics to explain how the subject has been used to further our understanding in some key areas. A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. This book is the first textbook treatment of a significant part of these results. It focuses on so-called equivariant methods, based on the Borsuk-Ulam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level. No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained.

A Journey Through Discrete Mathematics

Author: Martin Loebl
Publisher: Springer
ISBN: 9783319444796
Release Date: 2017-10-11
Genre: Computers

This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.

Geometric Combinatorics

Author: Ezra Miller
Publisher: American Mathematical Soc.
ISBN: 0821886959
Release Date:
Genre: Mathematics

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.

Algebraic and Geometric Combinatorics

Author: Christos A. Athanasiadis
Publisher: American Mathematical Soc.
ISBN: 9780821840801
Release Date: 2006
Genre: Mathematics

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.

SIAM Journal on Computing

Author: Society for Industrial and Applied Mathematics
Publisher:
ISBN: UOM:39015065057740
Release Date: 2006
Genre: Electronic data processing