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Home > Vol 2, No 3 (1993)

Tadeusz Józefiak and Bruce E. Sagan

We prove that various subarrangements of Coxeter hyperplane arrangements are free. We do this by exhibiting a basis for the corresponding module of derivations. Our method uses a theorem of Saito [24] and Terao [30] which checks for a basis using certain divisibility and determinantal criteria. As a corollary, we find the roots of the characteristic polynomials for these arrangements, since they are just one more than the degrees in any basis of the module. We will also see some interesting applications of symmetric and supersymmetric functions along the way.

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