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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0001-2,
author = {Toufik Mansour and Mark Shattuck},
title = {A combinatorial proof of a result for permutation pairs},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {797-806},
zbl = {1239.05017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0001-2}
}
Toufik Mansour; Mark Shattuck. A combinatorial proof of a result for permutation pairs. Open Mathematics, Tome 10 (2012) pp. 797-806. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0001-2/
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