Partially 2-Colored Permutations and the Boros-Moll Polynomials

William Y. C. Chen; Sabrina X. M. Pang; Ellen X. Y. Qu

paper

Partially 2-Colored Permutations and the Boros-Moll Polynomials

arXiv:1008.4740

Abstract

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.

9 pages