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Coxeter matroid : ウィキペディア英語版
Coxeter matroid
In mathematics, Coxeter matroids are generalization of matroids depending on a choice of a Coxeter group ''W'' and a parabolic subgroup ''P''. Ordinary matroids correspond to the case when ''P'' is a maximal parabolic subgroup of a symmetric group ''W''. They were introduced by , who named them after H. S. M. Coxeter.
give a detailed account of Coxeter matroids.
==Definition==

Suppose that ''W'' is a Coxeter group, generated by a set ''S'' of involutions, and ''P'' is a parabolic subgroup (the subgroup generated by some subset of ''S''). A Coxeter matroid is a subset of ''W''/''P'' that for every ''w'' in ''W'' contains a unique minimal element with respect to the ''w''-Bruhat order.

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