论文标题
弗里森（Frierson
Frierson's 1907 Parameterization of Compound Magic Squares Extended to Orders 3^{l}, l=1,2,3,..., with Information Entropy
论文作者
论文摘要
弗里森（Frierson）使用了订单3联想魔术平方的模式的强大参数化来构建一个由六个相关订单9化合物（或复合）魔法正方形的家族，其中一些是古老的。受Bellew的1997年扩展到27阶的刺激，我们将这些想法扩展到了所有命令的所有订单，此外，还为所有这些订单找到了矩阵光谱和熵措施的简单公式。该结构是分形的，我们给出了243顺序的数值结果，该订单显示了一个信息熵度量，即最低熵成员的恒定值约为1.168 ..。我们还简要考虑将Order 4 Magic Square具有最低熵的复合，为此，我们发现与恒定熵相似的趋势。
Frierson used a powerful parameterization of the pattern of the order 3 associative magic square to construct a family of six related order 9 compound (or composite) magic squares, several of them ancient. Stimulated by Bellew's 1997 extension to order 27, we extend these ideas to all orders that are powers of 3, and in addition find simple formulae for the matrix spectra and entropic measures for all those orders. This construction is fractal and we give numerical results to order 243 which show an information entropy measure converging to a constant value of about 1.168.. for the lowest entropy members. We also briefly consider compounding of an order 4 magic square with the lowest entropy, for which we find a similar trend to constant entropy.
