Higher Order Log-Concavity in Euler's Difference Table

William Y. C. Chen; Cindy C. Y. Gu; Kevin J. Ma; Larry X. W. Wang

Higher Order Log-Concavity in Euler's Difference Table

Combinatorics 2009-11-17 v1

Authors: William Y. C. Chen , Cindy C. Y. Gu , Kevin J. Ma , Larry X. W. Wang

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 $0\leq k \leq n$ , 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.

Keywords

collatz conjecture combinatorial bounds and extremal problems

Cite

@article{arxiv.0911.2775,
  title  = {Higher Order Log-Concavity in Euler's Difference Table},
  author = {William Y. C. Chen and Cindy C. Y. Gu and Kevin J. Ma and Larry X. W. Wang},
  journal= {arXiv preprint arXiv:0911.2775},
  year   = {2009}
}

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11 pages

Higher Order Log-Concavity in Euler's Difference Table

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