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Abstrakty
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.
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Kategorie tematyczne
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Czasopismo
Rocznik
Tom
Numer
Strony
797-806
Opis fizyczny
Daty
wydano
2012-04-01
online
2012-01-18
Twórcy
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
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0001-2