The Eulerian distribution on involutions is indeed unimodal |
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| Authors: | Victor JW Guo |
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| Institution: | Institut Camille Jordan, Université Claude Bernard (Lyon I), F-69622, Villeurbanne Cedex, France |
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| Abstract: | 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 |
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| Keywords: | Involutions Descent number Unimodality Eulerian polynomial Zeilberger's algorithm |
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