The Eulerian distribution on involutions is indeed unimodal

نویسندگان

  • Victor J. W. Guo
  • Jiang Zeng
چکیده

Let In,k (respectively, Jn,k) be the number of involutions (respectively, fixed-point free involutions) of {1, . . . , n} with k descents. Motivated by Brenti’s conjecture which states that the sequence In,0, In,1, . . . , In,n−1 is log-concave, we prove that the two sequences In,k and J2n,k are unimodal in k, for all n. Furthermore, we conjecture that there are nonnegative integers an,k such that n−1 ∑ k=0 In,kt k = b(n−1)/2c

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عنوان ژورنال:
  • J. Comb. Theory, Ser. A

دوره 113  شماره 

صفحات  -

تاریخ انتشار 2006