# Perfect $\langle k, r \rangle$-latin squares

Hare, Kevin G. (2000) Perfect $\langle k, r \rangle$-latin squares. [Preprint]

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A \textbf{\kr} $A = (a_{i,j})$ of order $n$ with $m$ elements is an $n \times n$ array in which each element occurs in each row and column, and the element $a_{i,j}$ occurs either $k$ times in row $i$ and $r$ times in column $j$,or occurs $r$ times in row $i$ and $k$ times in column $j$.In 1989, Cai, Kruskal, Liu and Shen studied the existence of \kr s.Here, a simpler construction of \kr s is given.