Cyclic permutations avoiding patterns in both one-line and cycle forms

Kassie Archer; Ethan Borsh; Jensen Bridges; Christina Graves; Millie Jeske

Cyclic permutations avoiding patterns in both one-line and cycle forms

Combinatorics 2024-09-04 v2

Authors: Kassie Archer , Ethan Borsh , Jensen Bridges , Christina Graves , Millie Jeske

Abstract

Let $\sigma$ and $\tau$ be patterns of length three; that is $\sigma, \tau \in \{123,132,213,231,312,321\}$ . In this paper, we enumerate the set of cyclic permutations in $\mathcal{S}_n$ that avoid $\sigma$ in their one-line notation and another pattern $\tau$ in their cycle notation.

Keywords

pattern avoidance in permutations permutations

Cite

@article{arxiv.2312.05145,
  title  = {Cyclic permutations avoiding patterns in both one-line and cycle forms},
  author = {Kassie Archer and Ethan Borsh and Jensen Bridges and Christina Graves and Millie Jeske},
  journal= {arXiv preprint arXiv:2312.05145},
  year   = {2024}
}

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