论文信息 - On overlarge sets of Kirkman triple systems

On overlarge sets of Kirkman triple systems

The determination of the existence of large sets of Kirkman triple systems (LKTS) is a classical combinatorial problem. In this paper we introduce a new concept OLGKS-overlarge sets of generalized Kirkman triple systems and show the relationship between the new concept and overlarge sets of Kirkman triple systems (OLKTS(v)). Further, some recursive constructions for OLGKS are given, and some new existence results of OLKTS(v) with a special properties are obtained, which plays an important role in the discussion of large sets of Kirkman triple systems.

Landang Yuan | Qingde Kang

[1] Gennian Ge,et al. Some new large sets of KTS(v) , 1999, Ars Comb..

[2] Luc Teirlinck,et al. Some new 2-resolvable Steiner quadruple systems , 1994, Des. Codes Cryptogr..

[3] Landang Yuan,et al. A tripling construction for overlarge sets of KTS , 2009, Discret. Math..

[4] Lijun Ji. A construction for large sets of disjoint Kirkman triple systems , 2007, Des. Codes Cryptogr..

[5] R. H. F. Denniston,et al. Sylvester's problem of the 15 schoolgirls , 1974, Discret. Math..

[7] Shengyuan Zhang,et al. An improved product construction for large sets of Kirkman triple systems , 2003, Discret. Math..

[8] Landang Yuan,et al. Some infinite families of large sets of Kirkman triple systems , 2008 .

[9] Lijun Ji,et al. Further results on large sets of Kirkman triple systems , 2008, Discret. Math..

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

[11] Zihong Tian,et al. Large sets of oriented triple systems with resolvability , 2000, Discret. Math..

[12] Arthur Cayley,et al. The Collected Mathematical Papers: On the Triadic Arrangements of Seven and Fifteen Things , 1850 .

[13] Jian-guo Lei. On large sets of Kirkman systems with holes , 2002, Discret. Math..