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A Unified Treatment of the Geometric Algebra of Matroids and Even Δ-Matroids

✍ Scribed by Walter Wenzel

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
288 KB
Volume
22
Category
Article
ISSN
0196-8858

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✦ Synopsis

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 as introduced by I. M. Gelfand and V. V. Serganova is slightly different, although for many important classes of W and P one gets the same structures. In the present paper, we extend the concept of the Tutte group of an ordinary matroid to combinatorial W P U -geometries and suggest two equivalent definitions of a W P Umatroid with coefficients in a fuzzy ring K. While the first one is more appropriate for many theoretical considerations, the second one has already been used to show that W P U -matroids with coefficients encompass matroids with coefficients and -matroids with coefficients.

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