Enumeration of some classes of words avoiding two generalized patterns of length three

TL;DR

This paper adapts a permutation pattern avoidance enumeration method to words, enabling the counting of various classes of words that avoid two specific generalized patterns of length three.

Contribution

It introduces a novel adaptation of permutation enumeration techniques to words, expanding the scope of pattern avoidance analysis.

Findings

Enumerated classes of words avoiding two generalized patterns of length three

Extended permutation pattern methods to word enumeration

Provided explicit counts for specific pattern-avoiding word classes

Abstract

The method we have applied in "A. Bernini, L. Ferrari, R. Pinzani, Enumerating permutations avoiding three Babson-Steingrimsson patterns, Ann. Comb. 9 (2005), 137--162" to count pattern avoiding permutations is adapted to words. As an application, we enumerate several classes of words simultaneously avoiding two generalized patterns of length 3.