Towards a solution of Archdeacon's conjecture on integer Heffter arrays
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929429613117440 |
|---|---|
| author | Pellegrini, Marco Antonio Traetta, Tommaso |
| author_facet | Pellegrini, Marco Antonio Traetta, Tommaso |
| contents | In this paper, we make significant progress on a conjecture proposed by Dan Archdeacon on the existence of integer Heffter arrays $H(m,n;s,k)$ whenever the necessary conditions hold, that is, $3\leqslant s \leqslant n$, $3\leqslant k\leqslant m$, $ms=nk$ and $nk\equiv 0,3 \pmod 4$. By constructing integer Heffter array sets, we prove the conjecture in the affirmative whenever $k\geqslant 7\cdot \gcd(s,k)$ is odd and $s\neq 3,5,6,10$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15183 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards a solution of Archdeacon's conjecture on integer Heffter arrays Pellegrini, Marco Antonio Traetta, Tommaso Combinatorics 05B20, 05B30 In this paper, we make significant progress on a conjecture proposed by Dan Archdeacon on the existence of integer Heffter arrays $H(m,n;s,k)$ whenever the necessary conditions hold, that is, $3\leqslant s \leqslant n$, $3\leqslant k\leqslant m$, $ms=nk$ and $nk\equiv 0,3 \pmod 4$. By constructing integer Heffter array sets, we prove the conjecture in the affirmative whenever $k\geqslant 7\cdot \gcd(s,k)$ is odd and $s\neq 3,5,6,10$. |
| title | Towards a solution of Archdeacon's conjecture on integer Heffter arrays |
| topic | Combinatorics 05B20, 05B30 |
| url | https://arxiv.org/abs/2407.15183 |