BOUNDARIES OF COXETER MATROIDS

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 (a lso known as WP-matroids) for Wand P, where P varies through all the p roper standard parabolic subgroups of W (Theorem 3 of the paper). A re markably simple interpretation of Coxeter matroids as certain sets of faces of the generalized permutahedron associated with the Coxeter gro up W (Theorem 1) yields a natural definition of the boundary of a Coxe ter matroid. The latter happens to be a union of Coxeter matroids for maximal standard parabolic subgroups Q(1) of P (Theorem 2). These resu lts have very natural interpretations in the case of ordinary matroids and flag-matroids (Section 3). (C) 1996 Academic Press, Inc.