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.

Abstract. We obtain a unification of two refinements of Euler's partition theorem respectively due to Bessenrodt and Glaisher. A specialization of Bessenrodt's insertion algorithm for a generalization of the Andrews-Olsson partition identity is used in our combinatorial construction.