2006/02/13 by Shinji Tanimoto, Tanimoto, Shinji
Mathematics · #05A05 #20B30 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A05 #msc:20B30
paper · pdf · doi:10.48550/arxiv.math/0602263
9 pages
arxiv created 2006/02/13 · arxiv updated 2009/12/01
The numbers of even and odd permutations with a given ascent number are investigated using an operator that was previously introduced by the author. Their difference is called a signed Eulerian number. By means of the operator the recurrence relation for signed Eulerian numbers is deduced, which was obtained by an analytic method. Our approach is straightforward and enables us to deduce other properties including divisibility by prime powers.