Geodesic
Basic derivations for subarrangements of Coxeter arrangements
Journal of Algebraic Combinatorics, Tome 2 (1993) no. 3, pp. 291-320.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : Primary, 52B30;, Secondary, 13B10,, 13C10,, 05E15,, 20F55,, 51F15
Keywords: hyperplane arrangement, derivation, basis, Coxeter 
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     title = {Basic derivations for subarrangements of {Coxeter} arrangements},
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Józefiak, Tadeusz; Sagan, Bruce E. Basic derivations for subarrangements of Coxeter arrangements. Journal of Algebraic Combinatorics, Tome 2 (1993) no. 3, pp. 291-320. http://geodesic.mathdoc.fr/item/JAC_1993__2_3_a0/