The problem studied in this article is the directed Kirkman packing,the resolvable directed packing which requires all blocks to be of size three except that,each resolution class should contain either one block of si...The problem studied in this article is the directed Kirkman packing,the resolvable directed packing which requires all blocks to be of size three except that,each resolution class should contain either one block of size two(when v≡2(mod 3)) or one block of size four (when v≡1 (mod 3)).A directed Kirkman packing design DKPD(v) is a resolvable directed packing of a v-set by the maximum possible number of resolution classes of this type.This article investigates the spectrum of DKPD(v) and it is found that it contains all positive integers v≥3 and v≠5,6.展开更多
It is proved in this paper that,for any given positive integer k≥2,there exists a constant v0=v0(k) such that for v≥v0,the necessary condition v=0 (mod k(k-)) for the existence of a nearly Kirkman system NKS (2,k,v)...It is proved in this paper that,for any given positive integer k≥2,there exists a constant v0=v0(k) such that for v≥v0,the necessary condition v=0 (mod k(k-)) for the existence of a nearly Kirkman system NKS (2,k,v) is also sufficient.Thus we have completely determined the asymptotic existence of NKS.展开更多
In this paper,we investigate the intersection numbers of nearly Kirkman triple systems.J_N [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 intersec...In this paper,we investigate the intersection numbers of nearly Kirkman triple systems.J_N [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 J_N[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 left undecided.展开更多
文摘The problem studied in this article is the directed Kirkman packing,the resolvable directed packing which requires all blocks to be of size three except that,each resolution class should contain either one block of size two(when v≡2(mod 3)) or one block of size four (when v≡1 (mod 3)).A directed Kirkman packing design DKPD(v) is a resolvable directed packing of a v-set by the maximum possible number of resolution classes of this type.This article investigates the spectrum of DKPD(v) and it is found that it contains all positive integers v≥3 and v≠5,6.
基金Project supported by the National Natural Sdence Foundation of China
文摘It is proved in this paper that,for any given positive integer k≥2,there exists a constant v0=v0(k) such that for v≥v0,the necessary condition v=0 (mod k(k-)) for the existence of a nearly Kirkman system NKS (2,k,v) is also sufficient.Thus we have completely determined the asymptotic existence of NKS.
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.J_N [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 J_N[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 left undecided.
