Emerging consecutive pattern avoidance

2025/11/04 by Hassler, Nathanaël, Kirgizov, Sergey
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Genome Rearrangement Algorithms

paper · pdf · doi:10.48550/arxiv.2511.02442

openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/08/01

Abstract

In this note we study the \em asymptotic popularity, that is, the limit probability to find a given consecutive pattern at a random position in a random permutation in the eighteen classes of permutations avoiding at least two length 3 consecutive patterns. We show that for ten classes, this popularity can be readily deduced from the structure of permutations. By combining analytical and bijective approaches, we study in details two more involved cases. The problem remains open for five classes.

Citations

• Pattern statistics in faro words and permutations
• Patterns in random permutations avoiding the pattern 321
• On multi-avoidance of generalized patterns
• Simultaneous avoidance of generalized patterns
• Generalised Pattern Avoidance

Related

• A probabilistic approach to consecutive pattern avoiding in permutations
• Asymptotic enumeration of permutations avoiding generalized patterns
• Patterns in random permutations avoiding some sets of multiple patterns
• The Expected Number of Distinct Consecutive Patterns in a Random Permutation
• Counting Consecutive Pattern Matches in S_n(132) and S_n(123)