A combinatorial proof of a result for permutation pairs

Toufik Mansour; Mark Shattuck

doi:10.2478/s11533-012-0001-2

A combinatorial proof of a result for permutation pairs

Toufik Mansour, Mark Shattuck

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	797-806
Number of pages	10
Journal	Central European Journal of Mathematics
Volume	10
Issue number	2
DOIs	https://doi.org/10.2478/s11533-012-0001-2
State	Published - Apr 2012

Keywords

Combinatorial proof
Exponential generating function
Permutations

ASJC Scopus subject areas

General Mathematics

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10.2478/s11533-012-0001-2

Cite this

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A combinatorial proof of a result for permutation pairs

Abstract

Keywords

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