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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.15685 |
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| _version_ | 1866929642456219648 |
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| author | Buratti, Marco Pasotti, Anita |
| author_facet | Buratti, Marco Pasotti, Anita |
| contents | The shiftable Heffter arrays are naturally generalized to the shiftable Heffter spaces. We present a recursive construction which starting from a single shiftable Heffter space leads to infinitely many other shiftable Heffter spaces of the same degree. We also present a direct construction making use of pandiagonal magic squares leading to a shiftable $(16\ell^2,4l;3)$ Heffter space for any $\ell \geq 1$. Combining these constructions we obtain a shiftable $(16\ell^2mn, 4\ell n; 3)$ Heffter space for every triple of positive integers $(\ell,m,n)$ with $m \geq n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15685 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shiftable Heffter spaces Buratti, Marco Pasotti, Anita Combinatorics The shiftable Heffter arrays are naturally generalized to the shiftable Heffter spaces. We present a recursive construction which starting from a single shiftable Heffter space leads to infinitely many other shiftable Heffter spaces of the same degree. We also present a direct construction making use of pandiagonal magic squares leading to a shiftable $(16\ell^2,4l;3)$ Heffter space for any $\ell \geq 1$. Combining these constructions we obtain a shiftable $(16\ell^2mn, 4\ell n; 3)$ Heffter space for every triple of positive integers $(\ell,m,n)$ with $m \geq n$. |
| title | Shiftable Heffter spaces |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.15685 |