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arXiv · 2001.06711

The Heritage of Cayley-Sudoku Tables

Kady Hossner Boden·Michael B. Ward
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Abstract

A Cayley-Sudoku table of a finite group G is a Cayley table for G subdivided into uniformly sized rectangular blocks, in such a way that each group element appears once in each block. They were introduced by J. Carmichael, K. Schloeman, and M. B. Ward [CSW], who also gave three ways to construct them. This paper has four aims. First, we review Constructions 1 and 2 of [CSW] and uncover their unexpected heritage in the work of R. Baer and J. Denes. Next we turn to some new instances of Construction 2 inspired by Baer, which answer an open question in [CSW]. Third, we provide a very brief outline of recent reinventions of special cases of Construction 1 in the literature. We conclude with an invitation to seek out the heritage of Construction 3. Portions of this paper appear in: Kady Hossner Boden and Michael B. Ward (2019) A New Class of Cayley-Sudoku Tables, Mathematics Magazine, 92:4, 243-251, DOI: 10.1080/0025570X.2019.1613949

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Kady Hossner Boden, Michael B. Ward. 2020-01-18. The Heritage of Cayley-Sudoku Tables. https://arxiv.org/abs/2001.06711

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