Generating functions for descents over words which avoid a consecutive pattern

TL;DR

This paper extends a mathematical method to analyze the distribution of descents in words that avoid certain consecutive patterns, providing new tools for combinatorial enumeration.

Contribution

It generalizes the reciprocity method to handle words avoiding patterns with at most one descent, advancing combinatorial pattern avoidance techniques.

Findings

Extended reciprocity method for pattern-avoiding words

Derived generating functions for descent distributions

Enhanced understanding of pattern avoidance in words

Abstract

In this paper, we extend the reciprocity method introduced by Jones and Remmel to study the distributions of descents over words which have no u-matches for words u that have at most one descent.