严格单纯Mendelsohn三元系的相交数

Intersections of Pure Mendelsohn Triple Systems

讨论严格单纯 Mendelsohn三元系的相交数问题 ,并证明了当 v≥ 1 9时 ,对任一正整数 v≡ 0 ,1 ( mod 3) ,存在两个严格单纯的 MTS( v)相交于 s个循环三元组的充要条件是 s∈ {0 ,1 ,2 ,… ,tv- 6,tv- 4,tv},其中 tv=v( v- 1 ) /3.

The intersection problem of pure Mendelsohn triple systems was almost completely solved in this paper, namely, it is proved that for any v ≡0,1(mod 3), v ≥19, there exists a pair of pure MTS(v) s intersecting in s cyclic triples if and only if s ∈｛0,1,2,…, t v -6,t v-4,t v ｝ where t v=v(v-1)/3 .