| Autor: |
Cavenagh, Nicholas J., Dinitz, Jeff, Donovan, Diane, Yazıcı, Sule |
| Rok vydání: |
2018 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
A Heffter array $H(n;k)$ is an $n\times n$ matrix such that each row and column contains $k$ filled cells, each row and column sum is divisible by $2nk+1$ and either $x$ or $-x$ appears in the array for each integer $1\leq x\leq nk$. Heffter arrays are useful for embedding the graph $K_{2nk+1}$ on an orientable surface. An integer Heffter array is one in which each row and column sum is $0$. Necessary and sufficient conditions (on $n$ and $k$) for the existence of an integer Heffter array $H(n;k)$ were verified by Archdeacon, Dinitz, Donovan and Yaz\i c\i \ (2015) and Dinitz and Wanless (2017). In this paper we consider square Heffter arrays that are not necessarily integer. We show that such Heffter arrays exist whenever $3\leq k
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| Databáze: |
arXiv |
| Externí odkaz: |
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