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We show that $\Gamma$-free fillings and lonesum fillings of Ferrers shapesare equinumerous by applying a previously defined bijection on matrices forthis more general case and by constructing a new bijection between Callansequences and Dumont-like permutations. As an application, we give a newcombinatorial interpretation of Genocchi numbers in terms of Callan sequences.Further, we recover some of Hetyei's results on alternating acyclictournaments. Finally, we present an interesting result in the case of certainother special shapes.

Lonesum and $\Gamma$-free $0$-$1$ fillings of Ferrers shapes