๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Construction of large sets of pairwise disjoint transitive triple systems II

โœ Scribed by C.C Lindner

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
563 KB
Volume
65
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 pairwise disjoint TI'Ss of order 2 + v, then there -exists a large set of pairwise disjoint TI'Ss of order 2 + vn. Two consequences of this result are the existence of a large set of pairwise disjoint TI'Ss of every odd admissible order and the existence of a large set of pairwise disjoint TI'Ss of every admissible order ~1000, except possibly 130 and 258.

๐Ÿ“œ SIMILAR VOLUMES

Further results about large sets of disj
Further results about large sets of disjoint Mendelsohn triple systems
โœ Qingde Kang; Yanxun Chang ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 374 KB

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