Faces of a Hyperplane Arrangement Enumerated by Ideal Dimension, with Application to Plane, Plaids, and Shi |
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| Authors: | Thomas Zaslavsky |
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| Affiliation: | (1) Department of Mathematical Sciences, Binghamton University, PO Box 6000, Binghamton, NY, 13902-6000, U.S.A. |
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| Abstract: | The ideal dimension of a real affine set is the dimension of the intersection of its projective topological closure with the infinite hyperplane. We obtain a formula for the number of faces of a real hyperplane arrangement having given dimension and ideal dimension. We apply the formula to the plane, to plaids, which are arrangements of parallel families in general position, and to affinographic arrangements. We compare two definitions of ideal dimension and ask about a complex analog of the enumeration. |
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| Keywords: | additive real gain graph affinographic arrangement arrangement of hyperplanes characteristic polynomial extended Catalan arrangement extended Linial arrangement extended Shi arrangement face count geometric semilattice graphic lift matroid ideal dimension plaid arrangement Whitney-number polynomial |
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