Frame自正交拉丁方中的截态

Transversals in Frame Self-orthogonal Latin Squares

本文证明当ｐ为质数幂时．在型为２ｐ的Ｆｒａｍｅ自正拉丁方中存在２（Ｐ－１）个互不相交的截态，且（ｉ）当ｐ大于３且时ｐ≡１（ｍｏｄ４）时这２（ｐ－１）个截态表现为ｐ－１个自对称的截态和（ｐ－１）／２对相互对称的截态；（ｉｉ）当ｐ大于５且ｐ≡３（ｍｏｄ４）时这２（ｐ－１）个截态在现为ｐ－１对相互对称的截态．

In this Paper,we show that there exist 2(p-1)disjoint transversals in a frame self-orthogonal latin square of type 2p and(i) occurring as p-1 symmetric ones and gsymmetric pairs when p is a prime power exceeding 3 and p=1(mod 4);(ii)occurring as p- 1 symmetric pairs when p is a prime power exceeding 5 and p=3(mod 4).