Recently, Brualdi et al. defined a partial order on an interesting class of binary matrices which generalizes the classical Bruhat order on the symmetric group, seen as the set of permutation matrices. We study the structure of this poset, and we give some enumerative results, e.g. about the maximal length of a chain and the largest size of an antichain.

This is a joint work with Carlos Martins da Fonseca and Ricardo Mamede.