Journal of Integer Sequences, Vol. 23 (2020), Article 20.6.3

Crossings over Permutations Avoiding Some Pairs of Patterns of Length Three

Paul M. Rakotomamonjy, Sandrataniaina R. Andriantsoa, and Arthur Randrianarivony
Department of Mathematics and Computer Science
Domain of Sciences and Technology
University of Antananarivo


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 other pairs of patterns of length three, we find relationships between the polynomial distributions of the crossings over permutations that avoid the pairs containing the pattern 231 on the one hand, and the pattern 312 on the other hand.

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(Concerned with sequences A007318 A076791 A299927.)

Received December 20 2019; revised versions received May 16 2020; May 17 2020; May 20 2020. Published in Journal of Integer Sequences, June 9 2020.

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