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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 $Q_{n,k}$ arelog-concave. For this, we introduce the notion of strong synchronisation andratio-alternating which are motivated by the notion of synchronisation andratio-dominance, introduced by Gross, Mansour, Tucker and Wang in 2014.  We show similar results for Type B Coxeter Groups. We finish with someconjectures to emphasize the following: though strong synchronisation isstronger than log-concavity, many pairs of interesting combinatorial familiesof sequences seem to satisfy this property.

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