Supported by National Natural Science Foundation of China(Grant Nos.11471096 and 11771119)
In this article, we establish the existence of an LHMTS(mv) for v ≡ 2 (mod 6) and m≡ 3 (mod 6). Thus there exists an LHMTS(mv) if and only if v(v-1)m2 ≡ 0 (mod 3) except possibly for v=6, m≡ 1, 5 (mo...
supported by National Natural Science Foundation of China (Grant No.60873267);Zhejiang Provincial Natural Science Foundation of China (Grant No. Y607026); sponsored by K. C. Wong Magna Fund in Ningbo University;the third author is supported by NSERC Grant OGP 0005320
Let v be a positive integer and let K be a set of positive integers. A (v, K, 1)-Mendelsohn design, which we denote briefly by (v, K, 1)-MD, is a pair (X, B) where X is a v-set (of points) and B is a collectio...
Supported by National Natural Science Foundation of China (Grant No.10771051)
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) ...
the National Natural Science Foundation of China(No.10671055);Natural Science Foundation of Hebei(No.A2007000230)
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...
This work was partially supported by the Tianyuan Mathematics Foundation of NSFC(Grant No.10526032);the Natural Science Foundation of Universities of Jiangsu Province(Grant No.05KJB110111).
An oriented tetrahedron is a set of four vertices and four cyclic triples with the property that any ordered pair of vertices is contained in exactly one of the cyclic triples. A tetrahedral quadruple system of order ...
This paper determined the existence of λ-fold pure Mendelsohn triple system of order v satisfying λv(v-1)≡0 (mod 3) and v≥4λ+5, or v=2λ+2, and in the case of λ=4,5,6,which completely settled their existence.