论文标题
排 - 哈米尔顿的拉丁广场和法尔科纳品种
Row-Hamiltonian Latin squares and Falconer varieties
论文作者
论文摘要
A \ Emph {Latin Square}是符号的矩阵，使每个符号在每个行和列中恰好发生一次。如果每对$ l $的不同行诱导的置换是一个完整的循环排列，则拉丁广场$ l $是\ emph {row-hamiltonian}。排 - 哈米尔顿的拉丁广场等于完美的$ 1 $ factorisation total tagrite图。我们第一次展示了一个拉丁正方形的家庭，这些平方是排名式的 - 哈米尔顿人，并且还确切地实现了作为柱 - 汉密尔顿或象征 - 汉密尔顿的相关特性之一。这个家庭允许我们构建非平凡，反社会性，同位素$ l $ claped的循环品种，以解决Falconer在1970年提出的空旷问题。
A \emph{Latin square} is a matrix of symbols such that each symbol occurs exactly once in each row and column. A Latin square $L$ is \emph{row-Hamiltonian} if the permutation induced by each pair of distinct rows of $L$ is a full cycle permutation. Row-Hamiltonian Latin squares are equivalent to perfect $1$-factorisations of complete bipartite graphs. For the first time, we exhibit a family of Latin squares that are row-Hamiltonian and also achieve precisely one of the related properties of being column-Hamiltonian or symbol-Hamiltonian. This family allows us to construct non-trivial, anti-associative, isotopically $L$-closed loop varieties, solving an open problem posed by Falconer in 1970.
