三个相互正交的4K＋2阶幂等拉丁方

Three Mutually Orthogonal Idempotent Latin Squares Of Order 4K+2

已经知道，对于任意的阶ｎ＞５，ｎ≠６，１０，１８，２２，２６，存在三个相互正交的幂等拉丁方．对于ｎ为６和１０的情况已确知其不存在，本文给出三个相互正交的１８，２２和２６阶幂等拉丁方，这样，三个相互正交幂等拉丁方的存在性问题已全部解决．

It is known that there are three mutually orthogonal idempotent Latinsquares of order n for any integer n≥5and n≠6,10,18,22,26.Clearly, there existneither orthogonal Latin squares of order 6 nor three orthogonal idempotent Latin squaresof order 10.In this paper,we give out three mutually orthogonal idempotent Latinsquares of order 18,22 and 26,so that the problem on exists of them have been resolvedcompletely.