共查询到20条相似文献,搜索用时 0 毫秒
1.
Zi-hong TIAN~ 《中国科学A辑(英文版)》2007,50(10):1369-1381
A directed triple system of order v,denoted by DTS(v,λ),is a pair(X,B)where X is a v- set and B is a collection of transitive triples on X such that every ordered pair of X belongs toλtriples of B.An overlarge set of disjoint DTS(v,λ),denoted by OLDTS(v,λ),is a collection{(Y\{y},A_i)}_i, such that Y is a(v 1)-set,each(Y\{y},A_i)is a DTS(v,λ)and all A_i's form a partition of all transitive triples of Y.In this paper,we shall discuss the existence problem of OLDTS(v,λ)and give the following conclusion:there exists an OLDTS(v,λ)if and only if eitherλ=1 and v≡0,1(mod 3),orλ=3 and v≠2. 相似文献
2.
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. 相似文献
3.
The spectrum for large sets of pure directed triple systems 总被引:1,自引:0,他引:1
ZHOU Junling CHANG Yanxun & Jl Lijun Institute of Mathematics Beijing Jiaotong University Beijing China Department of Mathematics Suzhou University Suzhou China 《中国科学A辑(英文版)》2006,49(8):1103-1127
An LPDTS(ν) is a collection of 3(ν-2) disjoint pure directed triple systems on the same set ofνelements. It is showed in Tian's doctoral thesis that there exists an LPDTS(ν) forν=0,4 (mod 6),ν≥4. In this paper, we establish the existence of an LPDTS(ν) forν= 1,3 (mod 6),ν> 3. Thus the spectrum for LPDTS(ν) is completely determined to be the set {ν:ν= 0, 1 (mod 3),ν≥4}. 相似文献
4.
A family ( X, B1 ), (X, B2 ), . . . , (X, Bq ) of q STS(v)s is a λ-fold large set of STS(v) and denoted by LSTS λ (v) if every 3-subset of X is contained in exactly λ STS(v)s of the collection. It is indecomposable and denoted by IDLSTS λ (v) if there does not exist an LSTS λ'(v) contained in the collection for any λ' λ. In this paper, we show that for λ = 5, 6, there is an IDLSTS λ (v) for v ≡ 1 or 3 (mod 6) with the exception IDLSTS6 (7). 相似文献
5.
《Discrete Mathematics》2020,343(2):111652
A Mendelsohn triple system MTS is a collection of cyclic triples (blocks) on a set of points. It is -balanced for when any two points, ordered pairs, or cyclic triples (resp.) are contained in the same or almost the same number of blocks (difference at most one). A -balanced Mendelsohn triple system is an MTS that is both 2-balanced and 3-balanced. Employing large sets of Mendelsohn triple systems and partitionable Mendelsohn candelabra systems, we completely determine the spectrum for which a 2-balanced Mendelsohn triple system exists. Meanwhile, we determine the existence spectrum for a -balanced Mendelsohn triple system. 相似文献
6.
A directed triple system of order v,denoted by DTS(v),is a pair (X,B) where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs to exactly one triple of B.A DTS(v) (X,A) is called pure and denoted by PDTS(v) if (a,b,c) ∈ A implies (c,b,a) ∈/ A.An overlarge set of PDTS(v),denoted by OLPDTS(v),is a collection {(Y \{yi},Aij) : yi ∈ Y,j ∈ Z3},where Y is a (v+1)-set,each (Y \{yi},Aij) is a PDTS(v) and these Ais form a partition of all transitive triples on Y .In this paper,we shall discuss the existence problem of OLPDTS(v) and give the following conclusion: there exists an OLPDTS(v) if and only if v ≡ 0,1 (mod 3) and v 3. 相似文献
7.
M.J. Grannell 《Discrete Mathematics》2009,309(14):4810-4818
A directed triple system of order v, , is a pair (V,B) where V is a set of v elements and B is a collection of ordered triples of distinct elements of V with the property that every ordered pair of distinct elements of V occurs in exactly one triple as a subsequence. A set of triples in a D is a defining set for D if it occurs in no other on the same set of points. A defining set for D is a smallest defining set for D if D has no defining set of smaller cardinality. In this paper we are interested in the quantity
8.
A large set of Kirkman triple systems of order v, denoted by LKTS(v), is a collection , where every is a KTS(v) and all form a partition of all triples on X. In this article, we give a new construction for LKTS(6v + 3) via OLKTS(2v + 1) with a special property and obtain new results for LKTS, that is there exists an LKTS(3v) for , where p, q ≥ 0, r
i
, s
j
≥ 1, q
i
is a prime power and mod 12.
相似文献
9.
Yuanyuan Liu 《Discrete Mathematics》2010,310(24):3619-3632
For three types of triples, unordered, cyclic and transitive, the corresponding extended triple, extended triple system and their large set are introduced. The spectrum of LEDTS(v) for even v has been given in our paper (Liu and Kang (2009) [9]). In this paper, we shall discuss the existence problem of LEDTS(v) for odd v and give the almost complete conclusion: there exists an LEDTS(v) for any positive integer v≠4 except possible v=95,143,167,203,215. 相似文献
10.
《Discrete Mathematics》2021,344(12):112619
An is a collection of disjoint pure Mendelsohn triple system on the same set of v elements. An is a special which contains exactly converse pairs of . In this paper, we mainly discuss the existence of an for and get the following conclusions: (1) there exists an if and only if and . (2) There exists an with index if and only if . 相似文献
11.
A large set of Kirkman triple systems of order v, denoted by LKTS(v), is a collection {(X, Bi) : 1 ≤ i ≤ v ? 2}, where every (X,Bi) is a KTS(v) and all Bi form a partition of all triples on X. Many researchers have studied the existence of LKTS(v) for a long time. In [13], the author introduced a concept—large set of generalized Kirkman systems (LGKS), which plays an important role in the discussion of LKTS. In this article, we give a new construction for LGKS and obtain some new results of LKTS, that is, there exists an LKTS(6u + 3) for u = qn, where n ≥ 1, q ≡ 7 (mod 12) and q is a prime power. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 202–212, 2008 相似文献
12.
An overlarge set of , denoted by , is a collection {(X?{x},Bx):x∈X}, where X is a (v+1)-set, each (X?{x},Bx) is a and {Bx:x∈X} forms a partition of all triples on X. In this paper, we give a tripling construction for overlarge sets of KTS. Our main result is that: If there exists an with a special property, then there exists an . It is obtained that there exists an for u=22n−1−1 or u=qn, where prime power q≡7 (mod 12) and m≥0,n≥1. 相似文献
13.
《Discrete Mathematics》2022,345(10):112969
An is a collection of pairwise disjoint on the same set of v elements. An is a special which contains exactly converse hexads of . In this paper, we mainly discuss the existence of an and get the following conclusions: (1) there exists an if and only if except possibly . (2) There exists an with index if and only if except possibly . 相似文献
14.
A Mendelsohn triple system of order v (MTS(v)) is a pair (X,B) where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS(v) (X,B) is called pure and denoted by PMTS(v) if (x, y, z) ∈ B implies (z, y, x) ∈B. A large set of MTS(v)s (LMTS(v)) is a collection of v - 2 pairwise disjoint MTS(v)s on a v-set. A self-converse large set of PMTS(v)s, denoted by LPMTS* (v), is an LMTS(v) containing [ v-2/2] converse pairs of PMTS(v)s. In this paper, some results about the existence and non-existence for LPMTS* (v) are obtained. 相似文献
15.
16.
Let X be a v-set, v≥3. A transitive triple (x,y,z) on X is a set of three ordered pairs (x,y),(y,z) and (x,z) of X. A directed triple system of order v, denoted by DTS(v), is a pair (X,?), where X is a v-set and ? is a collection of transitive triples on X such that every ordered pair of X belongs to exactly one triple of ?. A DTS(v) is called pure and denoted by PDTS(v) if (x,y,z)∈? implies (z,y,x)??. An overlarge set of disjoint PDTS(v) is denoted by OLPDTS(v). In this paper, we establish some recursive constructions for OLPDTS(v), so we obtain some results. 相似文献
17.
Lijun Ji 《Designs, Codes and Cryptography》2007,43(2-3):115-122
A Steiner system S(t, k, v) is called i-resolvable, 0 < i < t, if its block set can be partitioned into S(i, k, v). In this paper, a 2-resolvable S(3, 4, v) is used to construct a large set of disjoint Kirkman triple systems of order 3v − 3 (briefly LKTS) and some new orders for LKTS are then obtained.
Research supported by Tianyuan Mathematics Foundation of NSFC Grant 10526032 and Natural Science Foundation of Universities
of Jiangsu Province Grant 05KJB110111. 相似文献
18.
The determination of the possible numbers of triples in a maximal partial triple system of order begun by Severn is completed. The result rests on the characterization of the maximum number of edges in a triangle-free, nonbipartite, antieulerian graph onn vertices. 相似文献
19.
It has been shown by Lei, in his recent paper, that there exists a large set of Kirkman triple systems of order uv (LKTS(uv)) if there exist an LKTS(v), a TKTS(v) and an LR(u), where a TKTS(v) is a transitive Kirkman triple system of order v, and an LR(u) is a new kind of design introduced by Lei. In this paper, we improve this product construction by removing the condition “there exists a TKTS(v)”. Our main idea is to use transitive resolvable idempotent symmetric quasigroups instead of TKTS. As an application, we can combine the known results on LKTS and LR-designs to obtain the existence of an LKTS(3nm(2·13n1+1)(2·13nt+1)) for n1, m{1,5,11,17,25,35,43,67,91,123}{22r+125s+1 : r0,s0}, t0 and ni1 (i=1,…,t). 相似文献
20.
Yanxun Chang 《Discrete Mathematics》2009,309(20):5926-5931
We first define a transitive resolvable idempotent quasigroup (TRIQ), and show that a TRIQ of order v exists if and only if 3∣v and . Then we use TRIQ to present a tripling construction for large sets of resolvable Mendelsohn triple systems s, which improves an earlier version of tripling construction by Kang. As an application we obtain an for any integer n≥1, which provides an infinite family of even orders. 相似文献