A lozenge triangulation of the plane with integers
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909138055856128 |
|---|---|
| author | Bhat, Raghavendra N. Cobeli, Cristian Zaharescu, Alexandru |
| author_facet | Bhat, Raghavendra N. Cobeli, Cristian Zaharescu, Alexandru |
| contents | We introduce and study a three-folded linear operator depending on three parameters that has associated a triangular number tilling of the plane. As a result the set of all triples of integers is decomposed in classes of equivalence organized in four towers of two-dimensional triangulations. We provide the full characterization of the represented integers belonging to each network as families of certain quadratic forms. We note that one of the towers is generated by a germ that produces a covering of the plane with {Löschian} numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10500 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A lozenge triangulation of the plane with integers Bhat, Raghavendra N. Cobeli, Cristian Zaharescu, Alexandru Number Theory Combinatorics Primary 11B37, Secondary 11B50, 52C20 We introduce and study a three-folded linear operator depending on three parameters that has associated a triangular number tilling of the plane. As a result the set of all triples of integers is decomposed in classes of equivalence organized in four towers of two-dimensional triangulations. We provide the full characterization of the represented integers belonging to each network as families of certain quadratic forms. We note that one of the towers is generated by a germ that produces a covering of the plane with {Löschian} numbers. |
| title | A lozenge triangulation of the plane with integers |
| topic | Number Theory Combinatorics Primary 11B37, Secondary 11B50, 52C20 |
| url | https://arxiv.org/abs/2403.10500 |