A combinatorial proof of a result for permutation pairs

• Autorzy: Toufik Mansour , Mark Shattuck
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Exponential generating function; Combinatorial proof; Permutations

Kategorie tematyczne

• 05A05: Permutations, words, matrices
• 05A15: Exact enumeration problems, generating functions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 2
• Strony: 797-806

Daty

wydano

2012-04-01

online

2012-01-18

Twórcy

autor

Toufik Mansour

• University of Haifa

autor

Mark Shattuck

• University of Haifa

Bibliografia

• [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
• [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
• [5] Sloane N.J., The On-Line Encyclopedia of Integer Sequences, http://oeis.org
• [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
• [7] Stanley R.P., Enumerative Combinatorics, Vol. 1, Cambridge Stud. Adv. Math., 49, Cambridge University Press, Cambridge, 1997

Identyfikatory

DOI

10.2478/s11533-012-0001-2