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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.00141 |
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| _version_ | 1866913079631020032 |
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| author | Khrystik, M. A. |
| author_facet | Khrystik, M. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00141 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Combinatorics on finite words and the length of a finite-dimensional associative algebra Khrystik, M. A. Rings and Algebras 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. |
| title | Combinatorics on finite words and the length of a finite-dimensional associative algebra |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2605.00141 |