Permutations Almost Avoiding Monotone Distant Patterns

2025/11/26 by Nicholas Van Nimwegen, Van Nimwegen, Nicholas
Mathematics · #Advanced Combinatorial Mathematics #Limits and Structures in Graph Theory #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2511.20967

Abstract

In a previous work, Bóna and Pantone studied permutations that avoided all but one pattern of length k that began with a length k-1 increasing subsequence. We draw the connection between that idea and distant patterns, first discussed heavily in a work by Dimitrov, and study similar permutation classes, where the index not part of the increasing subsequence can vary. We find a large class of Wilf-Equivalences between k+1 classes of k patterns of length k+1, and outline several classes of unbalanced Wilf-Equivalences related to the first class. Using this, we are also find new bounds on the exponential growth rate on all monotone distant patterns with a single gap constraint.

Citations

• Permutations avoiding sets of patterns with long monotone subsequences
• On permutation patterns with constrained gap sizes
• Enumeration of small Wilf classes avoiding 1342 and two other 4-letter patterns
• Generating Permutations with Restricted Containers

Related

• Permutations avoiding sets of patterns with long monotone subsequences
• On permutation patterns with constrained gap sizes
• On the growth rate of the Stanley-Wilf limit of blockable permutations
• Where the monotone pattern (mostly) rules
• A short note on the Stanley-Wilf Conjecture for permutations on multisets