On relative simple Heffter spaces
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913728135430144 |
|---|---|
| author | Johnson, Laura Mella, Lorenzo Pasotti, Anita |
| author_facet | Johnson, Laura Mella, Lorenzo Pasotti, Anita |
| contents | In this paper, we introduce the concept of a relative Heffter space which simultaneously generalizes those of relative Heffter arrays and Heffter spaces. Given a subgroup $J$ of an abelian group $G$, a relative Heffter space is a resolvable configuration whose points form a half-set of $G\setminus{J}$ and whose blocks are all zero-sum in $G$. Here we present two infinite families of relative Heffter spaces satisfying the additional condition of being simple. As a consequence, we get new results on globally simple relative Heffter arrays, on mutually orthogonal cycle decompositions and on biembeddings of cyclic cycle decompositions of the complete multipartite graph into an orientable surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07445 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On relative simple Heffter spaces Johnson, Laura Mella, Lorenzo Pasotti, Anita Combinatorics In this paper, we introduce the concept of a relative Heffter space which simultaneously generalizes those of relative Heffter arrays and Heffter spaces. Given a subgroup $J$ of an abelian group $G$, a relative Heffter space is a resolvable configuration whose points form a half-set of $G\setminus{J}$ and whose blocks are all zero-sum in $G$. Here we present two infinite families of relative Heffter spaces satisfying the additional condition of being simple. As a consequence, we get new results on globally simple relative Heffter arrays, on mutually orthogonal cycle decompositions and on biembeddings of cyclic cycle decompositions of the complete multipartite graph into an orientable surface. |
| title | On relative simple Heffter spaces |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.07445 |