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Parity Alternating Permutations and Signed Eulerian Numbers
Shinji Tanimoto
Department of Mathematics, Kochi Joshi University, Kochi 780-8515, Japan
tanimoto@cc.kochi-wu.ac.jp
Annals of Combinatorics 14 (3) pp.355-366 September, 2010
AMS Subject Classification: 05A05, 20B35
Abstract:
This paper introduces subgroups of the symmetric group and studies their combinatorial properties. Their elements are called parity alternating, because they are permutations with even and odd entries alternately. The objective
of this paper is twofold. The first is to derive several properties of such permutations by subdividing them into even and odd permutations. The second is to discuss their combinatorial properties; among others, relationships between those permutations and signed Eulerian numbers. Divisibility properties by prime powers are also deduced for signed Eulerian numbers and several related numbers.
Keywords: Eulerian numbers, recurrence, permutations

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