Crossings over permutations avoiding some pairs of patterns of length three

Paul M. Rakotomamonjy, Sandrataniaina R. Andriantsoa, Arthur Randrianarivony

In this paper, we compute the distributions of the statistic number of crossings over permutations avoiding one of the pairs $\{321,231\}$, $\{123,132\}$ and $\{123,213\}$. The obt…