Crossings over permutations avoiding some pairs of three length-patterns

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

Published 2019-10-30Version 1

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 obtained results are new combinatorial interpretations of two known triangles in terms of restricted permutations statistic. For some pairs of three length-patterns, we find relationships between the polynomial distributions of the crossings over permutations that avoid the pairs containing the pattern 231 on the first hand and the pattern 312 on the other hand.