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{\bf Jacob A. White}
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{\bf On Multivariate Chromatic Polynomials of Hypergraphs and Hyperedge Elimination}
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In this paper we introduce multivariate hyperedge elimination polynomials and multivariate chromatic polynomials for hypergraphs. The first set of polynomials is defined in
terms of a deletion-contraction-extraction recurrence, previously investigated for graphs by Averbouch, Godlin, and Makowsky. The multivariate chromatic polynomial is an equivalent
polynomial defined in terms of colorings, and generalizes the coboundary polynomial of Crapo, and the bivariate chromatic polynomial of Dohmen, P\"onitz and Tittman.
We prove that specializations of
these new polynomials recover
polynomials which enumerate hyperedge coverings, matchings, transversals, and section hypergraphs, all weighted according to certain statistics.
We also prove that the polynomials can be defined in terms of M\"obius inversion on the partition lattice of a hypergraph, and we compute these polynomials for various classes of hypergraphs.
We also consider trivariate polynomials, which we call the hyperedge elimination polynomial and the trivariate chromatic polynomial.
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