Higher Order Log-Concavity in Euler's Difference Table

Abstract

Let $e_n^k$ be the entries in the classical Euler's difference table. We consider the array $d_n^k=e_n^k/k!$ for $0\le k\le n$, where $d_n^k$ can be interpreted as the number of k-fixed-points-permutations of [n]. We show that the sequence $\{d_n^k{\}}_{0\le k\le n}$ is 2-log-concave and reverse ultra log-concave for any given n.

11 pages

References in corpus (1)

• Fix-Euler-Mahonian statistics on wreath products