Displaying similar documents to “The combinatorics of the Al-Salam-Chihara q -Charlier polynomials.”

On Hultman numbers.

Doignon, Jean-Paul, Labarre, Anthony (2007)

Journal of Integer Sequences [electronic only]

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A combinatorial proof of a result for permutation pairs

Toufik Mansour, Mark Shattuck (2012)

Open Mathematics

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In this paper, a direct combinatorial proof is given of a result on permutation pairs originally due to Carlitz, Scoville, and Vaughan and later extended. It concerns showing that the series expansion of the reciprocal of a certain multiply exponential generating function has positive integer coefficients. The arguments may then be applied to related problems, one of which concerns the reciprocal of the exponential series for Fibonacci numbers.

Pattern avoiding partitions and Motzkin left factors

Toufik Mansour, Mark Shattuck (2011)

Open Mathematics

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Let L n, n ≥ 1, denote the sequence which counts the number of paths from the origin to the line x = n − 1 using (1, 1), (1, −1), and (1, 0) steps that never dip below the x-axis (called Motzkin left factors). The numbers L n count, among other things, certain restricted subsets of permutations and Catalan paths. In this paper, we provide new combinatorial interpretations for these numbers in terms of finite set partitions. In particular, we identify four classes of the partitions of...