Packing Density of Sets With Only Two Nonmixed Gaps
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_ | 1866916970939547648 |
|---|---|
| author | Natalchenko, Alexander Sagdeev, Arsenii |
| author_facet | Natalchenko, Alexander Sagdeev, Arsenii |
| contents | For a finite set of integers such that the first few gaps between its consecutive elements equal $a$, while the remaining gaps equal $b$, we study dense packings of its translates on the line. We obtain an explicit lower bound on the corresponding optimal density, conjecture its tightness, and prove it in case one of the gap lengths, $a$ or $b$, appears only once. This is equivalent to a Motzkin problem on the independence ratio of certain integer distance graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01101 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Packing Density of Sets With Only Two Nonmixed Gaps Natalchenko, Alexander Sagdeev, Arsenii Combinatorics Number Theory 05B40, 05C69, 11B05 For a finite set of integers such that the first few gaps between its consecutive elements equal $a$, while the remaining gaps equal $b$, we study dense packings of its translates on the line. We obtain an explicit lower bound on the corresponding optimal density, conjecture its tightness, and prove it in case one of the gap lengths, $a$ or $b$, appears only once. This is equivalent to a Motzkin problem on the independence ratio of certain integer distance graphs. |
| title | Packing Density of Sets With Only Two Nonmixed Gaps |
| topic | Combinatorics Number Theory 05B40, 05C69, 11B05 |
| url | https://arxiv.org/abs/2407.01101 |