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 ther...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.展开更多
In this paper, we investigate the intersection numbers of nearly Kirkman triple systems.JN[V] is the set of all integers k such that there is a pair of NKTS（v）s with a common uncovered collection of 2-subset interse...In this paper, we investigate the intersection numbers of nearly Kirkman triple systems.JN[V] is the set of all integers k such that there is a pair of NKTS（v）s with a common uncovered collection of 2-subset intersecting in k triples. It has been established that JN[v] = {0, 1,. v（v-2）/6-6,v（v-2）/6-4,v（v-2）/6} for any integers v = 0 （mod 6） and v ≥ 66. For v ≤ 60, there are 8 cases leftundecided.展开更多
基金supported by NSFC Grant 10671055NSFHB A2007000230Foundation of Hebei Normal University L2004Y11, L2007B22
文摘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.
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.2014JBM121)National Natural Science Foundation of China(Grant Nos.11271042,11471032 and 11571034)
文摘In this paper, we investigate the intersection numbers of nearly Kirkman triple systems.JN[V] is the set of all integers k such that there is a pair of NKTS（v）s with a common uncovered collection of 2-subset intersecting in k triples. It has been established that JN[v] = {0, 1,. v（v-2）/6-6,v（v-2）/6-4,v（v-2）/6} for any integers v = 0 （mod 6） and v ≥ 66. For v ≤ 60, there are 8 cases leftundecided.
