Higher Order Log-Concavity in Euler's Difference Table

Details Higher Order Log-Concavity in Euler's Difference Table Higher Order Log-Concavity in Euler's Difference Table

2009-11-14

arxiv.org/abs/0911.2775v1

Mathematics

Combinatorics

11 pages

Scientific paper

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 $0\leq k \leq n$, where $d_n^k$ can
be interpreted as the number of k-fixed-points-permutations of [n]. We show
that the sequence $\{d_n^k\}_{0\leq k\leq n}$ is 2-log-concave and reverse
ultra log-concave for any given n.

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