Further Results on Overlarge Sets of Kirkman Triple Systems  

作　　者：Lan Dang YUAN Qing De KANG 

机构地区：[1]College of Career Technology, Hebei Normal University, Shijiazhuang 050031, P. R. China [2]Institute of Mathematics, Hebei Normal University, Shijiazhuang 050016, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第3期419-434,共16页数学学报（英文版）

基　　金：supported by NSFC Grant 10671055;NSFHB A2007000230;Foundation of Hebei Normal University L2004Y11, L2007B22

摘　　要：In this paper, we introduce a new concept -- overlarge sets of generalized Kirkman systems （OLGKS）, research the relation between it and OLKTS, and obtain some new results for OLKTS. The main conclusion is： If there exist both an OLKF（6^k） and a 3-OLGKS（6^k-1,4） for all k ∈{6,7,...,40}／{8,17,21,22,25,26}, then there exists an OLKTS（v） for any v ≡ 3 （mod 6）, v ≠ 21. As well, we obtain the following result： There exists an OLKTS（6u ＋ 3） for u = 2^2n-1 - 1, 7^n, 31^n, 127^n, 4^r25^s, where n ≥ 1,r＋s≥ 1.In this paper, we introduce a new concept -- overlarge sets of generalized Kirkman systems （OLGKS）, research the relation between it and OLKTS, and obtain some new results for OLKTS. The main conclusion is： If there exist both an OLKF（6^k） and a 3-OLGKS（6^k-1,4） for all k ∈{6,7,...,40}／{8,17,21,22,25,26}, then there exists an OLKTS（v） for any v ≡ 3 （mod 6）, v ≠ 21. As well, we obtain the following result： There exists an OLKTS（6u ＋ 3） for u = 2^2n-1 - 1, 7^n, 31^n, 127^n, 4^r25^s, where n ≥ 1,r＋s≥ 1.

关 键 词：Kirkman frame Kirkman triple system overlarge set （2 1）-resolvable Steiner quadruplesystem 

分 类 号：O157.1[理学—数学]