可分解Mendelsohn三元系的相交数

Intersection Numbers of Resolvable Mendelsohn Triple Systems

证明了对于任意的正整数 v≡ 0 (mod 3) ,v≥ 63,存在两个 v阶可分解 Mendelsohn三元系相交于 s个公共循环三元组的充分必要条件是 s∈ { 0 ,1 ,… ,tv- 6,tv- 4 ,tv} ,其中 tv=v(v- 1 ) / 3.

It was proved that for any v≡0 (mod 3) and v ≥63, there exist two resolvable Mendelsohn triple systems of order v intersecting in s triples if and only if s∈(0,1,…,t v-6,t v-4,t v }, where t v=v(v-1)/3 .