A Completion of the Spectrum for the Overlarge Sets of Pure Mendelsohn Triple Systems

作者：Liu, Yuanyuan^*

来源：Graphs and Combinatorics, 2016, 32(3): 1077-1100.

DOI：10.1007/s00373-015-1635-1

• Overlarge set
• Pure
• Mendelsohn triple system

A pure Mendelsohn triple system of order v, denoted by PMTS(v), is a pair where X is a v-set and is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of and if implies . An overlarge set of PMTS(v), denoted by OLPMTS(v), is a collection , where Y is a -set, , each is a PMTS(v) and these s form a partition of all cyclic triples on Y. It is shown in [3] that there exists an OLPMTS(v) for (mod 6), , or (mod 12). In this paper, we shall discuss the existence problem of OLPMTS(v)s for (mod 12) and get the following conclusion: there exists an OLPMTS(v) if and only if (mod 3), and u not equal 6.

• 出版日期2016-5
• 单位北华航天工业学院