Characteristic and Ehrhart polynomials

Details Characteristic and Ehrhart polynomials Characteristic and Ehrhart polynomials

1998-01-02

arxiv.org/abs/math/9801008v1

J. Algebraic Combin. 7 (1998), 115-126

Mathematics

Combinatorics

16 pages, 1 figure, Latex, to be published in J. Alg. Combin. see related papers at http://www.math.msu.edu/~sagan

Scientific paper

Let A be a subspace arrangement and let chi(A,t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(B_n), where B_n is the type B Weyl arrangement, then chi(A,t) counts a certain set of lattice points. One can use this result to study the partial factorization of chi(A,t) over the integers and the coefficients of its expansion in various bases for the polynomial ring R[t]. Next we prove that the characteristic polynomial of any Weyl hyperplane arrangement can be expressed in terms of an Ehrhart quasi-polynomial for its affine Weyl chamber. Note that our first result deals with all subspace arrangements embedded in B_n while the second deals with all finite Weyl groups but only their hyperplane arrangements.

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