Parity-Alternate Permutations and Signed Eulerian Numbers

Details Parity-Alternate Permutations and Signed Eulerian Numbers Parity-Alternate Permutations and Signed Eulerian Numbers

2006-12-06

arxiv.org/abs/math/0612135v1

Mathematics

Combinatorics

11 pages

Scientific paper

In order to study signed Eulerian numbers, we introduce permutations of a particular type, called parity-alternate permutations, because they take even and odd entries alternately. The objective of this paper is twofold. The first is to derive several properties of those permutations, by subdividing them into even and odd ones. The second is to discuss relationships between those and signed Eulerian numbers. Divisibility properties by prime powers are also deduced for signed Eulerian numbers and several related numbers.

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