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arXiv · 2410.23216

Heffter arrays over partial loops

Raúl M. Falcón·Lorenzo Mella
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Abstract

A Heffter array over an additive group $G$ is any partially filled array $A$ satisfying that: (1) each one of its rows and columns sum to zero in $G$, and (2) if $i\in G\setminus\{0\}$, then either $i$ or $-i$ appears exactly once in $A$. In this paper, this notion is naturally generalized to that of $\mathcal{B}$-Heffter array over a partial loop, where $\mathcal{B}$ is a set of block-sum polynomials over an affine $1$-design on the set of entries in $A$.

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Raúl M. Falcón, Lorenzo Mella. 2024-10-30. Heffter arrays over partial loops. https://arxiv.org/abs/2410.23216

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