Partially 2-Colored Permutations and the Boros-Moll Polynomials
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.
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