Partially 2-Colored Permutations and the Boros-Moll Polynomials

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

2010-08-27

arxiv.org/abs/1008.4740v1

Mathematics

Combinatorics

9 pages

Scientific paper

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

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