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arXiv · 2605.00141

Combinatorics on finite words and the length of a finite-dimensional associative algebra

M. A. Khrystik
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Abstract

Let $f_W(n)$ be the number of different factors of length $n$ appearing in $W$. A classical result of Morse and Hedlund, stated in 1938, asserts that an infinite word $W$ is ultimately periodic if and only if $f_W(n)\leq n$ for some $n\in \mathbb N$. In this paper, we describe the form of finite words that satisfy the condition $f_W(n)\leq n$. We study relations between power avoidance and subword complexity of a finite word. We apply our combinatorial results to study the interrelations between various numerical invariants of finite-dimensional associative algebras.

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M. A. Khrystik. 2026-04-30. Combinatorics on finite words and the length of a finite-dimensional associative algebra. https://arxiv.org/abs/2605.00141

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