Pattern-avoiding stabilized-interval-free permutations

In this paper, we study pattern avoidance for stabilized-interval-free (SIF) permutations. These permutations are contained in the set of indecomposable permutations and in the set of derangements. We enumerate pattern-avoiding SIF permutations for classical and pairs of patterns of size 3. In parti...

Full description

Saved in:
Bibliographic Details
Published in:Discrete mathematics 2025-03, Vol.348 (3), p.114329, Article 114329
Main Authors: Birmajer, Daniel, Gil, Juan B., Tirrell, Jordan O., Weiner, Michael D.
Format: Article
Language:English
Subjects:
Derangement
Indecomposable
Pattern avoidance
Permutation
Stabilized-interval free
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we study pattern avoidance for stabilized-interval-free (SIF) permutations. These permutations are contained in the set of indecomposable permutations and in the set of derangements. We enumerate pattern-avoiding SIF permutations for classical and pairs of patterns of size 3. In particular, for the patterns 123 and 231, we rely on combinatorial arguments and the fixed-point distribution of general permutations avoiding these patterns. We briefly discuss 123-avoiding permutations with two fixed points and offer a conjecture for their enumeration by the distance between their fixed points. For the pattern 231, we also give a direct argument that uses a bijection to ordered forests.
ISSN:0012-365X
DOI:10.1016/j.disc.2024.114329