2006/12/06 by Shinji Tanimoto, Tanimoto, Shinji
Mathematics · Physics and Astronomy · #05A05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A05
paper · pdf · doi:10.48550/arxiv.math/0612135
11 pages
arxiv created 2006/12/06 · openalex publication_date 2006/12/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.