共查询到20条相似文献,搜索用时 0 毫秒
1.
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
2.
An LPMTS(v) is a collection of v-2 disjoint pure Mendelsohn triple systems on the same set of v elements. In this paper, the concept of t-purely partitionable Mendelsohn candelabra system (or t-PPMCS in short) is introduced for constructing LPMTS(v)s. A powerful recursive construction for t-PPMCSs is also displayed by utilizing s-fan designs. Together with direct constructions, the existence of an LPMTS(v) for and v>1 is established. For odd integer v?7, a special construction from both LPMTS(v) and OLPMTS(v) to LPMTS(2v+1) is set up. Finally, the existence of an LPMTS(v) is completely determined to be the set . 相似文献
3.
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
4.
An HMTS of type {n1, n2, ⋖, nh} is a directed graph which can be decomposed into 3-circuits. If the 3-circuits can be partitioned into parallel classes, then the HMTS is called an RHMTS. In this article it is shown that the RHMTSs of type mh exist when mh &equiv 0 (mod 3) and (m, h) &ne (1, 6), with the possible exception of h = 6 and , where M17 = {m|m is divisible by a prime less than 17}. The existence of Mendelsohn frames, which is closely related to RHMTS, is also considered in this article. It is proved that a Mendelsohn frame of type tu exists if and only if u ≥ 4 and t(u - 1) ≡ 0(mod 3) with 2 possible exceptions. © 1997 John Wiley & Sons, Inc. J Combin Designs 5:329–340, 1997 相似文献
5.
6.
Luc Teirlinck 《组合设计杂志》1999,7(5):311-315
In this article, we construct overlarge sets of disjoint S(3, 4, 3n − 1) and overlarge sets of disjoint S(3, 4, 3n + 1) for all n ≥ 2. Up to now, the only known infinite sequence of overlarge sets of disjoint S(3, 4, v) were the overlarge sets of disjoint S(3, 4, 2n) obtained from the oval conics of desarguesian projective planes of order 2n. © 1999 John Wiley & Sons, Inc. J Combin Design 7: 311–315, 1999 相似文献
7.
A Mendelsohn triple system (MTS) corresponds to an idempotent semisymmetric Latin square (quasigroup) of the same order. A holey MTS is called frame self-orthogonal, briefly FSOMTS, if its associated holey semisymmetric Latin square is frame self-orthogonal. In this paper, we use FSOMTS(hn) to denote an FSOMTS with n spanning holes of size h. The existence of FSOMTS(hn) for h3 has been known with a few exceptions. We extend the existing results and determine the necessary and sufficient conditions for the existence of FSOMTS(hn) for any h and n with some possible exceptions. 相似文献
8.
《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
9.
10.
《Discrete Mathematics》2021,344(12):112596
A holey Mendelsohn triple system (HMTS) is a decomposition of a complete multipartite directed graph into directed cycles of length 3. If the directed cycles of length 3 can be partitioned into parallel classes, then the HMTS is called an RHMTS. Bennett, Wei and Zhu [J. Combin. Des., 1997] showed that an RHMTS of type exists when and with some possible exceptions. In this paper, motivated by the application in constructing RHMTSs, we investigate the constructions of holey Mendelsohn frames. We prove that a 3-MHF of type exists if and only if , and , and then determine that the necessary condition for the existence of an RHMTS of type , namely, is also sufficient except for . New recursive constructions on incomplete RHMTSs via MHFs are introduced to settle this problem completely. 相似文献
11.
Alex W. Nowak 《组合设计杂志》2020,28(10):724-744
We define a Mendelsohn triple system (MTS) of order coprime with 3, and having multiplication affine over an abelian group, to be affine, nonramified. By exhibiting a one‐to‐one correspondence between isomorphism classes of affine MTS and those of modules over the Eisenstein integers, we solve the isomorphism problem for affine, nonramified MTS and enumerate these isomorphism classes (extending the work of Donovan, Griggs, McCourt, Opr?al, and Stanovský). As a consequence, all entropic MTSs of order coprime with 3 and distributive MTS of order coprime with 3 are classified. Partial results on the isomorphism problem for affine MTS with order divisible by 3 are given, and a complete classification is conjectured. We also prove that for any affine MTS, the qualities of being nonramified, pure, and self‐orthogonal are equivalent. 相似文献
12.
We extend our earlier work on overlarge sets of Fano planes, obtaining three results of particular interest. We find seven new partial geometries pg(8,7,4) and nine new strongly regular graphs, by means of switching cliques of points with spreads of lines. One of these new strongly regular graphs supports four different partial geometries. Then we give a new construction of the recently discovered eightfold cover of the complete graph K16.Supported by NSERC grant OGP0008651Supported by ARC grant A49130102 and an Australian Senior Research Fellowship 相似文献
13.
14.
Jianguo Lei 《组合设计杂志》2000,8(4):274-290
In this article, we study a large set of disjoint pure Mendelsohn triple systems “with holes” (briefly LPHMTS), which is a generalization of large set of disjoint pure Mendelsohn triple systems (briefly LPMTS), and give some recursive constructions on LPHMTS. Using these constructions, we show that there exists LPMTS(2n + 2) for any n ≠ 2. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 274–290, 2000 相似文献
15.
Yanxun Chang Giovanni Lo Faro Antoinette Tripodi Junling Zhou 《Discrete Mathematics》2012,312(8):1461-1467
An idempotent quasigroup of order is called resolvable (denoted by RIQ) if the set of non-idempotent 3-vectors can be partitioned into disjoint transversals. An overlarge set of idempotent quasigroups of order , briefly by OLIQ, is a collection of IQs, with all the non-idempotent 3-vectors partitioning all those on a -set. An OLRIQ is an OLIQ with each member IQ being resolvable. In this paper, it is established that there exists an OLRIQ for any positive integer , except for , and except possibly for . An OLIQ is another type of restricted OLIQ in which each member IQ has an idempotent orthogonal mate. It is shown that an OLIQ exists for any positive integer , except for , and except possibly for . 相似文献
16.
《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
17.
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
18.
19.
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
20.