Matrices with cyclically monotone rows and Cantor numeration systems
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915954778177536 |
|---|---|
| author | Šťovíček, Pavel Pelantová, Edita |
| author_facet | Šťovíček, Pavel Pelantová, Edita |
| contents | We study a class of square matrices with non-negative elements which have cyclically monotone rows in the sense that each row of a matrix from the class consists of a cyclically non-increasing sequence of numbers starting from a maximal element on the diagonal. We prove that if every diagonal element is strictly larger than all other elements in the respective row, then the matrix is regular. This property enables us to solve an open problem that comes from the theory of non-standard numeration systems, also called Cantor numeration systems. The problem concerns a one-to-one relationship between Cantor real bases, which are supposed to be alternate, that is, periodic with a period p, and lists of p sequences of non-negative integers satisfying the so-called Parry condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22344 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Matrices with cyclically monotone rows and Cantor numeration systems Šťovíček, Pavel Pelantová, Edita Number Theory 15B48, 11A67, 11C20 We study a class of square matrices with non-negative elements which have cyclically monotone rows in the sense that each row of a matrix from the class consists of a cyclically non-increasing sequence of numbers starting from a maximal element on the diagonal. We prove that if every diagonal element is strictly larger than all other elements in the respective row, then the matrix is regular. This property enables us to solve an open problem that comes from the theory of non-standard numeration systems, also called Cantor numeration systems. The problem concerns a one-to-one relationship between Cantor real bases, which are supposed to be alternate, that is, periodic with a period p, and lists of p sequences of non-negative integers satisfying the so-called Parry condition. |
| title | Matrices with cyclically monotone rows and Cantor numeration systems |
| topic | Number Theory 15B48, 11A67, 11C20 |
| url | https://arxiv.org/abs/2604.22344 |