Article ID Journal Published Year Pages File Type
8900501 Advances in Applied Mathematics 2018 21 Pages PDF
Abstract
We construct a new bijection between the set of n×k 0-1 matrices with no three 1's forming a Γ configuration and the set of (n,k)-Callan sequences, a simple structure counted by poly-Bernoulli numbers. We give two applications of this result: We derive the generating function of Γ-free matrices, and we give a new bijective proof for an elegant result of Aval et al. that states that the number of complete non-ambiguous forests with n leaves is equal to the number of pairs of permutations of {1,…,n} with no common rise.
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Physical Sciences and Engineering Mathematics Applied Mathematics
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