# A combinatorial proof of a result for permutation pairs

Open Mathematics (2012)

- Volume: 10, Issue: 2, page 797-806
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topToufik Mansour, and Mark Shattuck. "A combinatorial proof of a result for permutation pairs." Open Mathematics 10.2 (2012): 797-806. <http://eudml.org/doc/269732>.

@article{ToufikMansour2012,

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.},

author = {Toufik Mansour, Mark Shattuck},

journal = {Open Mathematics},

keywords = {Exponential generating function; Combinatorial proof; Permutations; exponential generating function; combinatorial proof; permutations},

language = {eng},

number = {2},

pages = {797-806},

title = {A combinatorial proof of a result for permutation pairs},

url = {http://eudml.org/doc/269732},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Toufik Mansour

AU - Mark Shattuck

TI - A combinatorial proof of a result for permutation pairs

JO - Open Mathematics

PY - 2012

VL - 10

IS - 2

SP - 797

EP - 806

AB - 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.

LA - eng

KW - Exponential generating function; Combinatorial proof; Permutations; exponential generating function; combinatorial proof; permutations

UR - http://eudml.org/doc/269732

ER -

## References

top- [1] Benjamin A.T., Quinn J.J., Proofs that Really Count, Dolciani Math. Exp., 27, Mathematical Association of America, Washington, 2003
- [2] Carlitz L., Scoville R., Vaughan T., Enumeration of pairs of permutations, Discrete Math., 1976, 14(3), 215–239 http://dx.doi.org/10.1016/0012-365X(76)90035-2 Zbl0322.05008
- [3] Fedou J.-M., Rawlings D., Statistics on pairs of permutations, Discrete Math., 1995, 143(1–3), 31–45 http://dx.doi.org/10.1016/0012-365X(94)00027-G
- [4] Langley T.M., Remmel J.B., Enumeration of m-tuples of permutations and a new class of power bases for the space of symmetric functions, Adv. in Applied Math., 2006, 36(1), 30–66 http://dx.doi.org/10.1016/j.aam.2005.05.005 Zbl1085.05068
- [5] Sloane N.J., The On-Line Encyclopedia of Integer Sequences, http://oeis.org Zbl1274.11001
- [6] Stanley R.P., Binomial posets, Möbius inversion, and permutation enumeration, J. Combinatorial Theory Ser. A, 1976, 20(3), 336–356 http://dx.doi.org/10.1016/0097-3165(76)90028-5 Zbl0331.05004
- [7] Stanley R.P., Enumerative Combinatorics, Vol. 1, Cambridge Stud. Adv. Math., 49, Cambridge University Press, Cambridge, 1997

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.