自反Mendelsohn设计SCMD(36t,9,1)的构造

The Construction of SCMD(36t,9,1)

Mendelsohn设计 MD(υ,k,λ)是一个对子 (X,B) ,其中 X为υ元集 ,B是 X的一个循环 k元组的集合 ,使得 X上任意由两不同元构成的有序对恰出现在 B的λ个区组中。若存在(X,B)到 (X,B-1)同构映射 ,则称 MD(υ,k,λ) =(X,B)为自反的。本文利用差和轨道的方法证明了 SCMD(36t,9,1 ) ,(其中 t为正整数 )

Mendelsohn design MD(υ,k,λ) is a pair(X,B),where X is a υ set together with a collection B of k tuples from X such that each ordered pair from X is contained in exactly λ k tuples of B.An MD(υ,k,λ) is said to be self converse,denoted by SCMD(υ,k,λ)=(X,B,f),if there is and isomorphic mapping f from (X,B)to (X,B -1 .In this paper,using the method of difference and orbit, a constructive proof for the existence of SCMD(36t,9,1)is given for any positive integer t.