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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Displaying similar documents to “Ascents of size less than d in compositions”
Longest alternating subsequences in pattern-restricted permutations.
A relationship between the major index for tableaux and the charge statistic for permutations.
Killpatrick, Kendra (2005)
The Electronic Journal of Combinatorics [electronic only]
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A bijective proof of a major index theorem of Garsia and Gessel.
Novick, Mordechai (2010)
The Electronic Journal of Combinatorics [electronic only]
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A combinatorial proof of a result for permutation pairs
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.
Two statistics linking Dyck paths and non-crossing partitions.
Zhao, Haijian, Zhong, Zheyuan (2011)
The Electronic Journal of Combinatorics [electronic only]
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Stein's method and descents after riffle shuffles.
Fulman, Jason (2005)
Electronic Journal of Probability [electronic only]
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Using homological duality in consecutive pattern avoidance.
Khoroshkin, Anton, Shapiro, Boris (2011)
The Electronic Journal of Combinatorics [electronic only]
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Permutations which avoid 1243 and 2143, continued fractions, and Chebyshev polynomials.
Egge, Eric S., Mansour, Toufik (2003)
The Electronic Journal of Combinatorics [electronic only]
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Explicit formulas for Bernoulli and Euler numbers.
Vella, David C. (2008)
Integers
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The combinatorics of the Garsia-Haiman modules for hook shapes.
Adin, Ron M., Remmel, Jeffrey B., Roichman, Yuval (2008)
The Electronic Journal of Combinatorics [electronic only]
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Statistics on the multi-colored permutation groups.
Bagno, Eli, Butman, Ayelet, Garber, David (2007)
The Electronic Journal of Combinatorics [electronic only]
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On a partition function of Richard Stanly.
Andrews, George E. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Pattern avoiding partitions and Motzkin left factors
Toufik Mansour, Mark Shattuck (2011)
Open Mathematics
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Let L n, n ≥ 1, denote the sequence which counts the number of paths from the origin to the line x = n − 1 using (1, 1), (1, −1), and (1, 0) steps that never dip below the x-axis (called Motzkin left factors). The numbers L n count, among other things, certain restricted subsets of permutations and Catalan paths. In this paper, we provide new combinatorial interpretations for these numbers in terms of finite set partitions. In particular, we identify four classes of the partitions of...