We show that $\Gamma$-free fillings and lonesum fillings of Ferrers shapes are equinumerous by applying a previously defined bijection on matrices for this more general case and by constructing a new bijection between Callan sequences and Dumont-like permutations. As an application, we give a new combinatorial interpretation of Genocchi numbers in terms of Callan sequences.Further, we recover some of Hetyei’s results on alternating acyclic tournaments. Finally, we present an interesting result in the case of certain other special shapes.

中文翻译：

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Lonesum和 $\Gamma$- 自由 $0$--$\mathrm{1个}$ 费雷尔形状的馅料

我们证明 $\Gamma$通过针对这种更一般的情况在矩阵上应用先前定义的双射，并在Callan序列和类似Dumont的置换之间构造新的双射，费勒形状的无填充和孤子填充是等价的。作为应用程序，我们根据Callan序列对Genocchi数进行了新的组合解释。此外，我们在交替的非循环锦标赛中恢复了Hetyei的一些结果。最后，在某些其他特殊形状的情况下，我们给出了一个有趣的结果。