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
topHow 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 ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.