Abstract
Let (X, ) be a Steiner triple system on v = |X| points, and suppose that is a partial parallel class (transversal, clear set, set of pairwise disjoint blocks) of maximum size . We want to derive a bound on . (I conjecture that in fact r is bounded, e.g., r ≦ 4 – 4 is attained for the Fano plane, but all that has been proved so far (cf. [1], [2]) are bounds r < C.v for some C. Here we shall prove r < 5v2/3.)Define a sequence of positive real numbers by q0 = Q · r2/v, , where l is determined by ql ≧ 6, , i.e.,(The constant Q will be chosen later.) Define inductively sets Ai, Ki and collections as follows. Let
Publisher
Canadian Mathematical Society
Cited by
16 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献