Combinatorics of the group of parity alternating permutations

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Combinatorics in the group of parity alternating permutations

We call a permutation parity alternating, if its entries assume even and odd integers alternately. Parity alternating permutations form a subgroup of the symmetric group. This paper deals with such permutations classified by two permutation statistics; the numbers of ascents and inversions. It turns out that they have a close relationship to signed Eulerian numbers. The approach is based on a s...

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Combinatorial study on the group of parity alternating permutations

The combinatorial theory for the set of parity alternating permutations is expounded. In view of the numbers of ascents and inversions, several enumerative aspects of the set are investigated. In particular, it is shown that signed Eulerian numbers have intimate relationships to the set.

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Parity-alternating permutations and successions

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 ...

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ژورنال

عنوان ژورنال: Advances in Applied Mathematics

سال: 2010

ISSN: 0196-8858

DOI: 10.1016/j.aam.2009.07.002