The longest increasing subsequence in involutions avoiding 3412 and another pattern

TL;DR

This paper investigates the average length of the longest increasing subsequence in involutions that avoid specific patterns, contributing to understanding permutation structures with pattern restrictions.

Contribution

It provides new insights into the mean length of the longest increasing subsequence in involutions avoiding 3412 and another pattern.

Findings

Determined the mean length for specific pattern-avoiding involutions.

Extended previous results on pattern-avoiding permutations.

Offered formulas or bounds for the expected LIS length.

Abstract

In this note, we study the mean length of the longest increasing subsequence of a uniformly sampled involution that avoids the pattern $3412$ and another pattern.