Equivalence Classes of Permutations Modulo Replacements Between 123 and\n Two-Integer Patterns

2013/09/18 by Vahid Fazel-Rezai, Fazel-Rezai, Vahid · 1 citation
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1309.4802

openalex publication_date 2013/09/18 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We explore a new type of replacement of patterns in permutations, suggested\nby James Propp, that does not preserve the length of permutations. In\nparticular, we focus on replacements between 123 and a pattern of two integer\nelements. We apply these replacements in the classical sense; that is, the\nelements being replaced need not be adjacent in position or value. Given each\nreplacement, the set of all permutations is partitioned into equivalence\nclasses consisting of permutations reachable from one another through a series\nof bi-directional replacements. We break the eighteen replacements of interest\ninto four categories by the structure of their classes and fully characterize\nall of their classes.\n

Citations

• Equivalence Classes of Permutations under Various Relations Generated by\n Constrained Transpositions

Cited by

• New Results on Pattern-Replacement Equivalences: Generalizing a Classical Theorem and Revising a Recent Conjecture

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