کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6423586 | 1342425 | 2011 | 7 صفحه PDF | دانلود رایگان |
For 0â¤kâ¤n, let enk be the entries in Euler's difference table and let dnk=enk/k!. Dumont and Randrianarivony showed enk equals the number of permutations on [n] whose fixed points are contained in {1,2,â¦,k}. Rakotondrajao found a combinatorial interpretation of the number dnk in terms of k-fixed-points-permutations of [n]. We show that for any nâ¥1, the sequence {dnk}0â¤kâ¤n is essentially 2-log-concave and reverse ultra log-concave.
⺠In this paper, we study the higher order log-concavity of {dnk}0â¤kâ¤n, where dnk=enk/n! and enk are the entries in Euler's difference table. ⺠We show that the sequence {dnk}0â¤kâ¤n is essentially 2-log-concave for any nâ¥1. ⺠We also show that the sequence {dnk}0â¤kâ¤n is reverse ultra log-concave for any nâ¥1.
Journal: Discrete Mathematics - Volume 311, Issue 20, 28 October 2011, Pages 2128-2134