Higher Order Log-Concavity in Euler's Difference Table

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

  Abstract:  Let ekn be the entries in the classical Euler's difference table. We consider the array dkn = ekn/k! for 0 ≤ k ≤ n, where dkn can be interpreted as the number of k-fixedpoints-permutations of [n]. We show that the sequence is 2-log-concave and reverse ultra log-concave for any given n.

  AMS Classification:  05A20; 33F10

  Keywords:  log-concavity, 2-log-concavity, reverse ultra log-concavity, Euler's difference table.

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