Combinatorics of the group of parity alternating permutations
نویسندگان
چکیده
منابع مشابه
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...
متن کاملCombinatorial 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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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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The group of alternating colored permutations is the natural analogue of the classical alternating group, inside the wreath product Zr ≀Sn. We present a ‘Coxeterlike’ presentation for this group and compute the length function with respect to that presentation. Then, we present this group as a covering of Z r 2 ≀ Sn and use this point of view to give another expression for the length function. ...
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There are numerous combinatorial objects associated to a Grassmannian permutationwλ that index cells of the totally nonnegative Grassmannian. We study some of these objects (rook placements, acyclic orientations, various restricted fillings) and their q-analogues in the case of permutations w that are not necessarily Grassmannian. Résumé. Il y a nombreaux objets combinatoires associés à une per...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2010
ISSN: 0196-8858
DOI: 10.1016/j.aam.2009.07.002