Log-concavity of the Excedance Enumerators in positive elements of Type A and Type B Coxeter Groups [article]

Hiranya Kishore Dey
2020 arXiv   pre-print
The classical Eulerian Numbers A_n,k are known to be log-concave. Let P_n,k and Q_n,k be the number of even and odd permutations with k excedances. In this paper, we show that P_n,k and Q_n,k are log-concave. For this, we introduce the notion of strong synchronisation and ratio-alternating which are motivated by the notion of synchronisation and ratio-dominance, introduced by Gross, Mansour, Tucker and Wang in 2014. We show similar results for Type B Coxeter Groups. We finish with some
more » ... es to emphasize the following: though strong synchronisation is stronger than log-concavity, many pairs of interesting combinatorial families of sequences seem to satisfy this property.
arXiv:2009.10655v2 fatcat:tlc6xlbwnvel7apyfrwgh6yt5q