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Parity-alternating permutations and successions

Augustine Munagi (2014)

Open Mathematics

The study of parity-alternating permutations of {1, 2, … n} is extended to permutations containing a prescribed number of parity successions - adjacent pairs of elements of the same parity. Several enumeration formulae are computed for permutations containing a given number of parity successions, in conjunction with further parity and length restrictions. The objects are classified using direct construction and elementary combinatorial techniques. Analogous results are derived for circular permutations....

Pattern avoiding partitions and Motzkin left factors

Toufik Mansour, Mark Shattuck (2011)

Open Mathematics

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 size n, all...

Pebblings.

Eriksson, Henrik (1995)

The Electronic Journal of Combinatorics [electronic only]

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