WELLDOC property for words generated by morphisms
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918380103008256 |
|---|---|
| author | Puzynina, Svetlana Schavelev, Vladimir |
| author_facet | Puzynina, Svetlana Schavelev, Vladimir |
| contents | In this paper, we study an abelian-type property of infinite words called well distributed occurrences, or WELLDOC for short. An infinite word $w$ on a $d$-ary alphabet has the WELLDOC property if, for each factor $u$ of $w$, positive integer $m$, and vector $v\in \mathbb{N}^d$, there is an occurrence of $u$ such that the Parikh vector of the prefix of $w$ preceding such occurrence is congruent to $v$ modulo $m$. The Parikh vector of a finite word $v$ on an alphabet has its $i$-th component equal to the number of occurrences of the $i$-th letter in $v$. We provide a criterion of the WELLDOC property for words generated by morphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08492 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | WELLDOC property for words generated by morphisms Puzynina, Svetlana Schavelev, Vladimir Discrete Mathematics Combinatorics 68R15 G.2.1 In this paper, we study an abelian-type property of infinite words called well distributed occurrences, or WELLDOC for short. An infinite word $w$ on a $d$-ary alphabet has the WELLDOC property if, for each factor $u$ of $w$, positive integer $m$, and vector $v\in \mathbb{N}^d$, there is an occurrence of $u$ such that the Parikh vector of the prefix of $w$ preceding such occurrence is congruent to $v$ modulo $m$. The Parikh vector of a finite word $v$ on an alphabet has its $i$-th component equal to the number of occurrences of the $i$-th letter in $v$. We provide a criterion of the WELLDOC property for words generated by morphisms. |
| title | WELLDOC property for words generated by morphisms |
| topic | Discrete Mathematics Combinatorics 68R15 G.2.1 |
| url | https://arxiv.org/abs/2603.08492 |