  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.
