Partially 2-Colored Permutations and the Boros-Moll Polynomials

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

Published 2010-08-27Version 1

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.