Matroids and Coxeter groups
نویسنده
چکیده
The paper describes a few ways in which the concept of a Coxeter group (in its most ubiquitous manifestation, the symmetric group) emerges in the theory of ordinary matroids: • Gale’s maximality principle which leads to the Bruhat order on the symmetric group; • Jordan–Hölder permutation which measures distance between two maximal chains in a semimodular lattice and which happens to be closely related to Tits’ axioms for buildings; • matroid polytopes and associated reflection groups; • Gaussian elimination procedure, BN-pairs and their Weyl groups. These observations suggest a very natural generalisation of matroids; the new objects are called Coxeter matroids and are related to other Coxeter groups in the same way as (classical) matroids are related to the symmetric group.
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