Oriented Matroids

Author: Anders Björner
Publisher: Cambridge University Press
ISBN: 052177750X
Release Date: 1999-11-18
Genre: Mathematics

First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.

Matroids A Geometric Introduction

Author: Gary Gordon
Publisher: Cambridge University Press
ISBN: 9781139536080
Release Date: 2012-08-02
Genre: Mathematics

Matroid theory is a vibrant area of research that provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the geometric approach to matroids. Written in a friendly, fun-to-read style and developed from the authors' own undergraduate courses, the book is ideal for students. Beginning with a basic introduction to matroids, the book quickly familiarizes the reader with the breadth of the subject, and specific examples are used to illustrate the theory and to help students see matroids as more than just generalizations of graphs. Over 300 exercises are included, with many hints and solutions so students can test their understanding of the materials covered. The authors have also included several projects and open-ended research problems for independent study.

New Perspectives in Algebraic Combinatorics

Author: Louis J. Billera
Publisher: Cambridge University Press
ISBN: 0521770874
Release Date: 1999-09-28
Genre: Mathematics

2000 text containing expository contributions by respected researchers on the connections between algebraic geometry, topology, commutative algebra, representation theory, and convex geometry.

Topics in Hyperplane Arrangements

Author: Marcelo Aguiar
Publisher: American Mathematical Soc.
ISBN: 9781470437114
Release Date: 2017-11-22
Genre: Algebraic spaces

This monograph studies the interplay between various algebraic, geometric and combinatorial aspects of real hyperplane arrangements. It provides a careful, organized and unified treatment of several recent developments in the field, and brings forth many new ideas and results. It has two parts, each divided into eight chapters, and five appendices with background material. Part I gives a detailed discussion on faces, flats, chambers, cones, gallery intervals, lunes and other geometric notions associated with arrangements. The Tits monoid plays a central role. Another important object is the category of lunes which generalizes the classical associative operad. Also discussed are the descent and lune identities, distance functions on chambers, and the combinatorics of the braid arrangement and related examples. Part II studies the structure and representation theory of the Tits algebra of an arrangement. It gives a detailed analysis of idempotents and Peirce decompositions, and connects them to the classical theory of Eulerian idempotents. It introduces the space of Lie elements of an arrangement which generalizes the classical Lie operad. This space is the last nonzero power of the radical of the Tits algebra. It is also the socle of the left ideal of chambers and of the right ideal of Zie elements. Zie elements generalize the classical Lie idempotents. They include Dynkin elements associated to generic half-spaces which generalize the classical Dynkin idempotent. Another important object is the lune-incidence algebra which marks the beginning of noncommutative Möbius theory. These ideas are also brought upon the study of the Solomon descent algebra. The monograph is written with clarity and in sufficient detail to make it accessible to graduate students. It can also serve as a useful reference to experts.

Combinatorial Reciprocity Theorems An Invitation to Enumerative Geometric Combinatorics

Author: Matthias Beck
Publisher: American Mathematical Soc.
ISBN: 9781470422004
Release Date: 2018-12-12
Genre: Combinatorial analysis

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.

Encyclopedia of Optimization

Author: Christodoulos A. Floudas
Publisher: Springer Science & Business Media
ISBN: 9780387747583
Release Date: 2008-09-04
Genre: Mathematics

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Spatial Information Theory Foundations of Geographic Information Science

Author: Werner Kuhn
Publisher: Springer
ISBN: UOM:39015048088598
Release Date: 2003-11-05
Genre: Computers

This book constitutes the refereed proceedings of the International Conference on Spatial Information Theory, COSIT 2003, held at Kartause Ittingen, Switzerland, in September 2003. The 26 revised full papers presented were carefully reviewed and selected from 61 submissions. The papers are organized in topical sections on ontologies of space and time, reasoning about distances and directions, spatial reasoning - shapes and diagrams, computational approaches, reasoning about regions, vagueness, visualization, and landmarks and wayfinding.

Interfaces

Author:
Publisher:
ISBN: UOM:39015035254575
Release Date: 1995
Genre: Industrial management


Arrangements

Author: Peter Orlik
Publisher: Amer Mathematical Society
ISBN: UOM:39015050696882
Release Date: 2000-06
Genre: Mathematics


Coxeter Matroids

Author: Alexandre V. Borovik
Publisher: Springer Science & Business Media
ISBN: 9781461220664
Release Date: 2012-12-06
Genre: Mathematics

Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory. In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians.

New Technical Books

Author: New York Public Library
Publisher:
ISBN: UOM:39015063566296
Release Date: 1994
Genre: Engineering