754 research outputs found

    Log-concavity of matroid h-vectors and mixed Eulerian numbers

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    For any matroid MM, we compute the Tutte polynomial TM(x,y)T_M(x,y) using the mixed intersection numbers of certain tautological classes in the combinatorial Chow ring Aβˆ™(M)A^\bullet(M) arising from Grassmannians. Using mixed Hodge-Riemann relations, we deduce a strengthening of the log-concavity of the h-vector of a matroid complex, improving on an old conjecture of Dawson whose proof was announced recently by Ardila, Denham and Huh.Comment: 29 pages, comments welcome
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