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Some infinite families of large sets of Kirkman triple systems

✍ Scribed by Landang Yuan; Qingde Kang

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
145 KB
Volume
16
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

A large set of Kirkman triple systems of order v, denoted by LKTS(v), is a collection {(X, B~i~) : 1 ≀ i ≀ vβ€‰βˆ’β€‰2}, where every (X,B~i~) is a KTS(v) and all B~i~ form a partition of all triples on X. Many researchers have studied the existence of LKTS(v) for a long time. In [13], the author introduced a conceptβ€”large set of generalized Kirkman systems (LGKS), which plays an important role in the discussion of LKTS. In this article, we give a new construction for LGKS and obtain some new results of LKTS, that is, there exists an LKTS(6__u__ + 3) for u = q^n^, where n β‰₯ 1, q ≑ 7 (mod 12) and q is a prime power. Β© 2007 Wiley Periodicals, Inc. J Combin Designs 16: 202–212, 2008

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