Partially 2-Colored Permutations and the Boros-Moll Polynomials

William Y.C. Chen, Sabrina X.M. Pang and Ellen X.Y. Qu

  Abstract:  We find a combinatorial setting for the coefficients of the Boros-Moll polynomials Pm(a) in terms of partially 2-colored permutations. Using this model, we give a combinatorial proof of a recurrence relation on the coefficients of Pm(a). This approach enables us to give a combinatorial interpretation of the log-concavity of Pm(a) which was conjectured by Moll and confirmed by Kauers and Paule.

  AMS Classification:  05A05, 05A10, 05A20

  Keywords:  partially 2-colored permutation, Boros-Moll polynomial, rising factorial, log-concavity, bijection

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