Large sets of oriented triple systems with resolvability

Kang, Qingde; Tian, Zihong

doi:10.1016/s0012-365x(99)00288-5

Cited by 23 publications

(13 citation statements)

References 13 publications

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“…Lemma 3.2 [4] . If there exists an S(3, K, v) and an OLDTS(k − 1) for every k ∈ K, then there exists an OLDTS(v − 1).…”

Section: Existence Of Oldts(v)mentioning

confidence: 99%

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The spectrum for overlarge sets of directed triple systems

Tian

2007

SCI CHINA SER A

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A directed triple system of order v, denoted by DTS(v, λ), is a pair (X, B) where X is a vset and B is a collection of transitive triples on X such that every ordered pair of X belongs to λ triplesand all Ai'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 either λ = 1 and v ≡ 0, 1 (mod 3), or λ = 3 and v = 2.

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“…Lemma 3.2 [4] . If there exists an S(3, K, v) and an OLDTS(k − 1) for every k ∈ K, then there exists an OLDTS(v − 1).…”

Section: Existence Of Oldts(v)mentioning

confidence: 99%

“…We have known that an overlarge set of DTS(v) contains three times number of "small" sets that an overlarge MTS(v) of the same type does, and a close relationship between MTSs and DTSs is revealed in [4,8,9].…”

Section: Recursive Constructionsmentioning

confidence: 99%

The spectrum for overlarge sets of directed triple systems

Tian

2007

SCI CHINA SER A

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“…In [13], we gave a method for constructing LDTS(v) from a known LMTS(v). Let (V, A) be an MTS(v), our method consists of the following four steps.…”

Section: Lrmtsmentioning

confidence: 99%

More large sets of resolvable MTS and DTS with even orders

Kang

Xu²

2008

Acta Math. Appl. Sin. Engl. Ser.

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In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q + 2, or LRMTS(2q + 2), where q = 6t + 5 is a prime power.Using a computer, we find examples of such structure for t ∈ T = {0, 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 18, 20, 22, 24}. Furthermore, by a method we introduced in [13], large set of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTS and LRDTS introduced in [2, 20, 21], and by the new results for LR-design in [8], we obtain the existence for LRMTS(v) and LRDT S(v), where v = 12(t + 1) m i ≥0(2 · 7 m i + 1)(2 · 13 n i + 1) and t ∈ T , which provides more infinite family for LRMTS and LRDTS of even orders.

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“…In [13], we give a method to construct an LDTS(v) from a known LMTS(v). For a given cyclic triple a, b, c , call the transitive triple (a, b, c) or (b, c, a) or (c, a, b) a cyclic shift of a, Obviously, BIG(v, A) is a cubic graph with an even number of vertices, since both |A| and |A| are even.…”

Section: Lrmts(v) −→ Lrdts(v)mentioning

confidence: 99%

“…LRDTS(v)). The existence of LRMTS(v)s and LRDTS(v)s has been investigated by Kang [8], Kang and Lei [12], Kang and Tian [13], Xu and Kang [18], Chang [2], Zhou and Chang [21,22] and Kang and Xu [14]. By their research and related results about large sets of Kirkman triple systems [3][4][5][6]15,19,20], we can list the known conclusions as follows.…”

Section: Introductionmentioning

confidence: 99%

More large sets of resolvable MTS and resolvable DTS with odd orders

Kang

Zhao

2008

Discrete Mathematics

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In this paper, we first give a method to construct large sets of resolvable Mendelsohn triple systems of order q +2, where q =6t +1 is a prime power. Then, using a computer, we find solutions for t ∈ T ={35, 38, 46, 47, 48, 51, 56, 60}. Furthermore, by a method we introduced, large sets of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTSs and LRDTSs, and by new results for LR-designs, we obtain the existence of an LRMTS(v) and an LRDTS(v) for all v of the formwhere t ∈ T and M and N are finite multisets of non-negative integers. This provides more infinite classes for LRMTSs and LRDTSs with odd orders.

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Large sets of oriented triple systems with resolvability

Cited by 23 publications

References 13 publications

The spectrum for overlarge sets of directed triple systems

The spectrum for overlarge sets of directed triple systems

More large sets of resolvable MTS and DTS with even orders

More large sets of resolvable MTS and resolvable DTS with odd orders

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