Heffter Spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929386955997184 |
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| author | Buratti, Marco Pasotti, Anita |
| author_facet | Buratti, Marco Pasotti, Anita |
| contents | The notion of a Heffter array, which received much attention in the last decade, is equivalent to a pair of orthogonal Heffter systems. In this paper we study the existence problem of a set of $r$ mutually orthogonal Heffter systems for any $r$. Such a set is equivalent to a resolvable partial linear space of degree $r$ whose parallel classes are Heffter systems: this is a new combinatorial design that we call a Heffter space. We present a series of direct constructions of Heffter spaces with block size odd and arbitrarily large degree $r$ obtained with the crucial use of finite fields. Among the applications we establish, in particular, the existence of $r$ mutually orthogonal $k$-cycle systems of order a prime power $q=2kw+1$ whenever $kw$ is odd and $w>4k^4\lceil{r\over k}\rceil$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03940 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Heffter Spaces Buratti, Marco Pasotti, Anita Combinatorics The notion of a Heffter array, which received much attention in the last decade, is equivalent to a pair of orthogonal Heffter systems. In this paper we study the existence problem of a set of $r$ mutually orthogonal Heffter systems for any $r$. Such a set is equivalent to a resolvable partial linear space of degree $r$ whose parallel classes are Heffter systems: this is a new combinatorial design that we call a Heffter space. We present a series of direct constructions of Heffter spaces with block size odd and arbitrarily large degree $r$ obtained with the crucial use of finite fields. Among the applications we establish, in particular, the existence of $r$ mutually orthogonal $k$-cycle systems of order a prime power $q=2kw+1$ whenever $kw$ is odd and $w>4k^4\lceil{r\over k}\rceil$. |
| title | Heffter Spaces |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.03940 |