论文信息 - Intersection Numbers of Kirkman Triple Systems

Intersection Numbers of Kirkman Triple Systems

LetJR(v) denote the set of all integersksuch that there exists a pair ofKTS(v) with preciselyktriples in common. In this article we determine the setJR(v) forv?3(mod6) (only 10 cases are left undecided forv=15, 21, 27, 33, 39) and establish thatJR(v)=I(v) forv?3(mod6) andv?45, whereI(v)={0, 1, ?, tv?6, tv?4, tv} andtv=16v(v?1).

Giovanni Lo Faro | Yanxun Chang

[1] Kevin T. Phelps,et al. A class of Steiner triple systems of order 21 and associated Kirkman systems , 1981 .

[2] Charles C. Lindner. Construction of Steiner triple systems having exactly one triple in common , 1974 .

[3] A. E. Brouwer,et al. Optimal packings of $K_4$'s into a K$_n$ : the case n $\equiv$ 5 (mod 6) , 1976 .

[4] Douglas R. Stinson,et al. A survey of Kirkman triple systems and related designs , 1991, Discret. Math..

[5] Alexander Rosa,et al. Steiner triple systems having a prescribed number of triples in common , 1975 .

[7] Andries E. Brouwer,et al. Optimal Packings of K4's into a Kn , 1979, J. Comb. Theory A.

[8] Alexander Rosa,et al. Intersection Properties of Steiner Systems , 1980 .

[9] Jean Doyen. Constructions of disjoint Steiner triple systems , 1972 .

[10] D. K. Ray-Chaudhuri,et al. Solution of Kirkman''s schoolgirl problem , 1971 .

[11] Luc Teirlinck,et al. On Making Two Steiner Triple Systems Disjoint , 1977, J. Comb. Theory, Ser. A.

[12] Douglas R. Stinson,et al. On the existence of Kirkman triple systems containing Kirkman subsystems , 1988 .