Longest alternating subsequences in pattern-restricted permutations.
Firro, Ghassan, Mansour, Toufik, Wilson, Mark C. (2007)
The Electronic Journal of Combinatorics [electronic only]
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Firro, Ghassan, Mansour, Toufik, Wilson, Mark C. (2007)
The Electronic Journal of Combinatorics [electronic only]
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Toufik Mansour, Mark Shattuck (2012)
Open Mathematics
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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.
Fulman, Jason (2004)
The Electronic Journal of Combinatorics [electronic only]
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Araújo, P.V. (1998)
Portugaliae Mathematica
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Deutsch, Emeric, Hildebrand, A.J., Wilf, Herbert S. (2003)
The Electronic Journal of Combinatorics [electronic only]
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Kiwi, Marcos, Loebl, Martin (2008)
The Electronic Journal of Combinatorics [electronic only]
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Maisoon Falah, Toufik Mansour (2011)
Open Mathematics
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A composition of a positive integer n is a finite sequence π1π2...πm of positive integers such that π1+...+πm = n. Let d be a fixed number. We say that we have an ascent of size d or more (respectively, less than d) if πi+1 ≥ πi+d (respectively, πi < πi+1 < πi + d). Recently, Brennan and Knopfmacher determined the mean, variance and limiting distribution of the number of ascents of size d or more in the set of compositions of n. In this paper, we find an explicit formula for the...
Firro, Ghassan, Mansour, Toufik (2006)
The Electronic Journal of Combinatorics [electronic only]
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Hegarty, Peter (2004)
The Electronic Journal of Combinatorics [electronic only]
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Novick, Mordechai (2010)
The Electronic Journal of Combinatorics [electronic only]
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Khoroshkin, Anton, Shapiro, Boris (2011)
The Electronic Journal of Combinatorics [electronic only]
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Elizalde, Sergi (2004)
The Electronic Journal of Combinatorics [electronic only]
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Kaiser, Tomáš, Klazar, Martin (2003)
The Electronic Journal of Combinatorics [electronic only]
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