Displaying similar documents to “Multiple pattern avoidance with respect to fixed points and excedances.”

A combinatorial proof of a result for permutation pairs

Toufik Mansour, Mark Shattuck (2012)

Open Mathematics


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.