On large sets of disjoint Steiner triple systems II
โ Scribed by Lu Jia-Xi
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 482 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0097-3165
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๐ SIMILAR VOLUMES
The maximum number of pairwise disjoint transitive triple systems (T'I'Ss) of order n is 3(n -2). Such a collection is called a large set of pairwise disjoint TI'Ss of order n. The main result in this paper is the proof of the following theorem: If n -1 or 5 (rood 6), and there exists a large set of
In this note, a construction of the large sets of pairwise disjoint Mendelsohn triple systems of order 72k + 6, where k > 1 and k F 1 or 2 (mod 3), is given. Let X be a set of v elements (v 2 3). A cyclic triple from X is a collection of three pairs (x, y), (y,z) and (z, x), where x,y and z are dis
Let D(u) be the maximum number of pairwk disjoint Steiner triple sysiems of order v. We prove that D(3v:r 2 2v + D(v) for every u = 1 oi 3 (mod 6), u 2 3. As a corollary, we have D(3n) -3n-2 for every n 2 1.