Equivalence classes of permutations modulo descents and left-to-right maxima

Baril, Jean-Luc; Petrossian, Armen

doi:10.1515/puma-2015-0002

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Cited by 2 publications

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“…Recently [3,4], two equivalence relations on permutations based on the excedance and descent statistics were introduced. The main results of these works consist of giving generating functions for the number of equivalence classes for several restricted sets of permutations such as involutions, cycles, DOI: 10.1515/puma-2015-0025 derangements, and permutations avoiding at most one pattern of length three.…”

Section: Introduction Definitions and Notationsmentioning

confidence: 99%

Forests and pattern-avoiding permutations modulo pure descents

Baril

Kirgizov

Petrossian

2018

Pure Mathematics and Applications

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We investigate an equivalence relation on permutations based on the pure descent statistic. Generating functions are given for the number of equivalence classes for the set of all permutations, and the sets of permutations avoiding exactly one pattern of length three. As a byproduct, we exhibit a permutation set in one-to-one correspondence with forests of ordered binary trees, which provides a new combinatorial class enumerated by the single-source directed animals on the square lattice. Furthermore, bivariate generating functions for these sets are given according to various statistics.

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Section: Introduction Definitions and Notationsmentioning

confidence: 99%