Higher order log-concavity in Euler’s difference table |
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Authors: | William YC Chen Cindy CY Gu Kevin J Ma Larry XW Wang |
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Institution: | aCenter for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, PR China |
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Abstract: | For 0≤k≤n, let be the entries in Euler’s difference table and let . Dumont and Randrianarivony showed equals the number of permutations on n] whose fixed points are contained in {1,2,…,k}. Rakotondrajao found a combinatorial interpretation of the number in terms of k-fixed-points-permutations of n]. We show that for any n≥1, the sequence is essentially 2-log-concave and reverse ultra log-concave. |
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Keywords: | Log-concavity 2-log-concavity Reverse ultra log-concavity Euler&rsquo s difference table |
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