Coxeter Matroids (Google eBook)
Springer, Jul 11, 2003 - Mathematics - 264 pages
Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry. This largely self-contained text provides an intuitive and interdisciplinary treatment of Coxeter matroids, a new and beautiful generalization of matroids which is based on a finite Coxeter group. Key topics and features: * Systematic, clearly written exposition with ample references to current research * Matroids are examined in terms of symmetric and finite reflection groups * Finite reflection groups and Coxeter groups are developed from scratch * The Gelfand-Serganova theorem is presented, allowing for a geometric interpretation of matroids and Coxeter matroids as convex polytopes with certain symmetry properties * Matroid representations in buildings and combinatorial flag varieties are studied in the final chapter * Many exercises throughout * Excellent bibliography and index Accessible to graduate students and research mathematicians alike, "Coxeter Matroids" can be used as an introductory survey, a graduate course text, or a reference volume.
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Boundaries of Coxeter Matroids - Borovik, Gelfand, White ...
The purpose of this paper is to introduce, for a finite Coxeter group W the mod boundary operator on the space of all Coxeter matroids also known as WP ...
The Greedy Algorithm and Coxeter Matroids
The main result of this paper is that for Coxeter matroids, just as for ordinary matroids, the greedy algorithm provides a solution to a naturally ...
Alexandre V. Borovik Research interests in Combinatorics
The general structural theory of Coxeter matroids is now reasonably well developed in works of Gelfand, White and myself, though most results are still in ...
www.maths.manchester.ac.uk/ ~avb/ combinatorics.html
Boundaries of Coxeter Matroids
mod 2 boundary operator on the space of all Coxeter matroids (also known as WP- ... Coxeter matroids as certain sets of faces of the generalized ...
linkinghub.elsevier.com/ retrieve/ pii/ S0001870896900389
A geometric characterization of Coxeter matroids
Coxeter matroids, introduced by Gelfand and Serganova, are combinatorial ... Coxeter matroids and their further generalizations were studied in [ 1-7, 15]. ...
www.springerlink.com/ index/ 949H534268X62103.pdf
MIMS eprints - 2007.48: Coxeter Matroids
This largely self-contained work provides an intuitive and interdisciplinary treatment of Coxeter matroids, a new and beautiful generalization of matroids ...
ingentaconnect An Adjacency Criterion for Coxeter Matroids
An Adjacency Criterion for Coxeter Matroids. Authors: Borovik A.1; Vince A.2. Source: Journal of Algebraic Combinatorics, Volume 9, Number 3, May 1999 , pp. ...
www.ingentaconnect.com/ content/ klu/ jaco/ 1999/ 00000009/ 00000003/ 00203299;jsessionid=2kb4etele0g3j.alexandra?format=print
White, Neil L.
On exchange properties for Coxeter matroids and oriented matroids. (English. ... The Coxeter matroids of Gelfand et al. (English. English summary) ...
www.math.ufl.edu/ fac/ facmr/ White.html
An Adjacency Criterion for Coxeter Matroids
(Theorem 1.2) concerns a geometric characterization of Coxeter matroids. ... Coxeter matroids were introduced (under the name of WP-matroids) by Gelfand and ...
www.springerlink.com/ index/ N6116JK53W750343.pdf
Fields Institute - The Coxeter Legacy
Coxeter matroids The talk will describe a variety of ways in which the concept ... The language of Coxeter groups and Coxeter matroids is very flexible and ...
www.fields.utoronto.ca/ programs/ scientific/ 03-04/ coxeterlegacy/ abstracts.html