Constructions for overlarge sets of disjoint pure directed triple systems |
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Authors: | Zihong Tian Shencai Xu |
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Institution: | 1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050016, People’s Republic of China 2. School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, 050061, People’s Republic of China
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Abstract: | 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. |
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