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arXiv · 1110.0162

On computation of the characteristic polynomials of the discriminantal arrangements and the arrangements generated by generic points

Yasuhide Numata·Akimichi Takemura
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Abstract

In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the discriminantal arrangement with the parameter (n,k) is isomorphic to the intersection lattice of the hyperplane arrangement generated by n generic points in the d-dimensional vector space where d=n-k-1. The combinatorics of the discriminantal arrangements is very hard, except for the special cases of the Boolean arrangements (k=0) and the braid arrangements (k=1). We review some results on the intersection lattices of the arrangements generated by generic points and use them to obtain some computational results on the characteristic polynomials of the discriminantal arrangements.

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Yasuhide Numata, Akimichi Takemura. 2011-10-02. On computation of the characteristic polynomials of the discriminantal arrangements and the arrangements generated by generic points. https://arxiv.org/abs/1110.0162

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