Counting words without strictly increasing subwords of fixed length

TL;DR

This paper derives exact formulas for counting n-ary words that avoid strictly increasing subwords of a fixed length, with applications to combinatorial enumeration.

Contribution

It introduces new exact formulas for generating functions that count words avoiding certain increasing subword patterns.

Findings

Derived explicit formulas for generating functions

Provided applications in combinatorial enumeration

Enhanced understanding of pattern-avoiding words

Abstract

In this paper, we derive exact formulas for generating functions counting the number of $n$-ary words avoiding strictly increasing subwords of length $k$, and provide some applications of these formulas.