Avoiding patterns in irreducible permutations

Abstract : We explore the classical pattern avoidance question in the case of irreducible permutations, i.e., those in which there is no index i such that sigma( i + 1) - sigma( i) = 1. The problem is addressed completely in the case of avoiding one or two patterns of length three, and several well known sequences are encountered in the process, such as Catalan, Motzkin, Fibonacci, Tribonacci, Padovan and Binary numbers. Also, we present constructive bijections between the set of Motzkin paths of length n - 1 and the sets of irreducible permutations of length n ( respectively fixed point free irreducible involutions of length 2 n) avoiding a pattern alpha for alpha is an element of {132, 213, 321}. This induces two new bijections between the set of Dyck paths and some restricted sets of permutations.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01418662
Contributeur : Le2i - Université de Bourgogne <>
Soumis le : vendredi 16 décembre 2016 - 18:10:48
Dernière modification le : mercredi 12 septembre 2018 - 01:26:22

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  • HAL Id : hal-01418662, version 1

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Jean-Luc Baril,. Avoiding patterns in irreducible permutations. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2016, 17 (3), pp.13-30. ⟨http://search.proquest.com/openview/b8caab9176a71645955cd4293f6499f1/1?pq-origsite=gscholar&cbl=946337⟩. ⟨hal-01418662⟩

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