论文标题
Cayley-Sudoku桌子的遗产
The Heritage of Cayley-Sudoku Tables
论文作者
论文摘要
有限组G的Cayley-Sudoku表是一个用于G分为均匀尺寸的矩形块的Cayley表，以使每个组元素在每个块中出现一次。他们是由J. Carmichael，K。Schloeman和M. B. Ward [CSW]介绍的，他们还提供了三种构建它们的方法。本文有四个目标。首先，我们回顾了[CSW]的结构1和2，并在R. Baer和J. Denes的作品中揭示了他们意外的遗产。接下来，我们转向一些受Baer启发的建筑2的新实例，该实例在[CSW]中回答了一个公开问题。第三，我们简要概述了文献中最新的特殊构建案例1。 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
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
