✦ LIBER ✦

Maurer's Homotopy Theory and Geometric Algebra for Even Δ-Matroids

✍ Scribed by Walter Wenzel

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 340 KB
Volume: 17
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.1996.0002

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✦ Synopsis

The Tutte group of a matroid M is a certain abelian group which controls the representability of M. The representation theory of matroids and that of even ⌬-matroids have much in common. This paper is devoted to the extension of the concept of the Tutte group to even ⌬-matroids defined on sets of arbitrary cardinality. Similarly as in ordinary matroid theory the Tutte group can be defined in several possible ways in terms of generators and relations.

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The concept of a combinatorial W P U -geometry for a Coxeter group W , a subset P of its generating involutions and a subgroup U of W with P ⊆ U yields the combinatorial foundation for a unified treatment of the representation theories of matroids and of even -matroids. The concept of a W P -matroid