The intersection numbers of KTSs with a common parallel class

摘要

In this paper, the intersection numbers of KTSs with a common parallel class are investigated. Denote by ~(J1)[u] the set of all integers k such that there is a pair of KTS(3u)s with a common parallel class intersecting in k+u triples, u of them being the triples of the common parallel class. It has been established that ~(J1)[u]=0,1,?,3(u2)-6,3(u2)-4,3(u2) for any odd integer u<7 and u≠9,11,13,17,19. For u=9,11,13,17,19, there are 11 cases that are left undecided.