Generalized Dellac configurations

Abstract

We study combinatorics of two generalizations of Dellac configurations. First, we establish a correspondence between a generalized Dellac configuration with three parameters and a generalized Dumont permutations. Secondly, by relaxing conditions on Dellac configurations, we introduce a generalization which we call Dellac configurations with boundaries. We show several recurrence relations for the Poincar\'e polynomials of Dellac configurations with boundaries.