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Boundaries of Coxeter Matroids

โœ Scribed by Alexandre V. Borovik; Israel Gelfand; Neil White

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
230 KB
Volume
120
Category
Article
ISSN
0001-8708

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โœฆ Synopsis

The purpose of this paper is to introduce, for a finite Coxeter group W, the mod 2 boundary operator on the space of all Coxeter matroids (also known as WPmatroids) for W and P, where P varies through all the proper standard parabolic subgroups of W (Theorem 3 of the paper). A remarkably simple interpretation of Coxeter matroids as certain sets of faces of the generalized permutahedron associated with the Coxeter group W (Theorem 1) yields a natural definition of the boundary of a Coxeter matroid. The latter happens to be a union of Coxeter matroids for maximal standard parabolic subgroups Q i of P (Theorem 2). These results have very natural interpretations in the case of ordinary matroids and flagmatroids (Section 3).

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