| Summary: | 碩士 === 東吳大學 === 數學系 === 91 === Abstract
An extended directed triple system of order n is a pair (V, B), where B is a collection of ordered triples from a n-set V(each ordered triple may have repeated elements) such that every ordered pair of elements of V, not necessarily distinct, is contained in exactly one ordered triple of B. The elements of B are called blocks. There are five types of blocks: (1)[a, b, c], (2)[a, b, a], (3)[a, a, b], (4)[b, a, a], (5)[a, a, a]. Let EDTS(n;b_2,b_1) denote the class of EDTS(n) in which the number of blocks of the form [a, b, a] is b_2 and the number of blocks of the form [a, a, b] or [b, a, a] is b_1. We will construct the classes EDTS(n;b_2,b_1) for all admissible b_1 and b_2 in Chapter 2.
Recently, Castellana and Raines prove that every extended Mendelsohn triple system of order v can be embedded in an extended Mendelsohn triple system of order n for all n>=2v . In Chapter 3, we prove that every extended directed system of order v can be embedded in an extended directed system of order n for all n>=2v .
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