Journal of Combinatorics

Volume 5 (2014)

Number 4

Equivalence classes of permutations modulo excedances

Pages: 453 – 469

DOI: http://dx.doi.org/10.4310/JOC.2014.v5.n4.a4

Authors

Jean-Luc Baril (Université de Bourgogne, Dijon, France)

Toufik Mansour (Department of Mathematics, University of Haifa, Israel)

Armen Petrossian (Université de Bourgogne, Dijon, France)

Abstract

We introduce a new equivalence relation on permutations where two permutations are equivalent if and only if they coincide on their excedance sets. This paper studies equivalence classes for several subsets of permutations. Enumerating results are presented for permutations, cycles and permutations avoiding one or two patterns of length three. Also, an open question is proposed.

Keywords

permutations, equivalence class, excedance, pattern, Bell, Motzkin, Catalan, Fibonacci numbers

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