### Partitions, rooks, and symmetric functions in noncommuting variables.

Can, Mahir Bilen, Sagan, Bruce E. (2011)

The Electronic Journal of Combinatorics [electronic only]

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Can, Mahir Bilen, Sagan, Bruce E. (2011)

The Electronic Journal of Combinatorics [electronic only]

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Chow, Chak-On (2008)

The Electronic Journal of Combinatorics [electronic only]

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Morris, A.O., Abdel-Aziz, A.A. (1996)

The Electronic Journal of Combinatorics [electronic only]

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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...

Ferenc Oravecz (2000)

Colloquium Mathematicae

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The lattice of partitions and the sublattice of non-crossing partitions of a finite set are important objects in combinatorics. In this paper another sublattice of the partitions is investigated, which is formed by the symmetric partitions. The measure whose nth moment is given by the number of non-crossing symmetric partitions of n elements is determined explicitly to be the "symmetric" analogue of the free Poisson law.

Adin, Ron M., Remmel, Jeffrey B., Roichman, Yuval (2008)

The Electronic Journal of Combinatorics [electronic only]

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Kreiman, Victor (2008)

The Electronic Journal of Combinatorics [electronic only]

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Bergeron, François, Lauve, Aaron (2010)

The Electronic Journal of Combinatorics [electronic only]

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Maróti, Attila (2003)

Integers

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Rowell, Michael, Yee, Ae Ja (2009)

Integers

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Vallejo, Ernesto (2009)

The Electronic Journal of Combinatorics [electronic only]

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Toufik Mansour, Mark Shattuck (2011)

Open Mathematics

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In this paper, we provide new combinatorial interpretations for the Pell numbers p n in terms of finite set partitions. In particular, we identify six classes of partitions of size n, each avoiding a set of three classical patterns of length four, all of which have cardinality given by p n. By restricting the statistic recording the number of inversions to one of these classes, and taking it jointly with the statistic recording the number of blocks, we obtain a new polynomial generalization...

Mendes, Anthony, Remmel, Jeffrey, Wagner, Jennifer (2004)

The Electronic Journal of Combinatorics [electronic only]

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