Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Pattern-restricted permutations of small order

Kassie Archer, Robert P. Laudone

Abstract

We enumerate 132-avoiding permutations of order 3 in terms of the Catalan and Motzkin generating functions, answering a question of Bóna and Smith from 2019. We also enumerate 231-avoiding permutations that are composed only of 3-cycles, 2-cycles, and fixed points.

Pattern-restricted permutations of small order

Abstract

We enumerate 132-avoiding permutations of order 3 in terms of the Catalan and Motzkin generating functions, answering a question of Bóna and Smith from 2019. We also enumerate 231-avoiding permutations that are composed only of 3-cycles, 2-cycles, and fixed points.
Paper Structure (5 sections, 19 theorems, 22 equations, 3 tables)

This paper contains 5 sections, 19 theorems, 22 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Background and notation
  3. Avoiding 231 with cycle lengths 1, 2, or 3
  4. 132-avoiding permutations of order 3
  5. Open Questions

Key Result

Theorem 3.1

If we let then

Theorems & Definitions (38)

  • Theorem 3.1
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Lemma 3.4
  • proof
  • Lemma 3.5
  • proof
  • Lemma 3.6
  • ...and 28 more