## Abstract We give a general construction for Steiner triple systems on a countably infinite point set and show that it yields 2 nonisomorphic systems all of which are uniform and __r__βsparse for all finite __r__β©Ύ4. Β© 2009 Wiley Periodicals, Inc. J Combin Designs 18: 115β122, 2010
Note on large sets of infinite steiner systems
β Scribed by Peter J. Cameron
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 250 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
β¦ Synopsis
Large sets of Steiner systems s ( t , k , n ) exist for all finite t and k with t < k and all infinite n. The vector space analogues exist over a field F for all finite t and k with f < R provided that either v or F is infinite, and n 1 2k -t + 1. This inequality is best possible. o 1995 John Wiley & Sons, Inc.
π SIMILAR VOLUMES
## Abstract A __large set__ of Kirkman triple systems of order __v__, denoted by __LKTS__(__v__), is a collection {(__X__, __B~i~__) : 1ββ€β__i__ββ€β__v__βββ2}, 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 th
In this article, we construct overlarge sets of disjoint S(3, 4, 3 n -1) and overlarge sets of disjoint S(3, 4, 3 n + 1) for all n β₯ 2. Up to now, the only known infinite sequence of overlarge sets of disjoint S(3, 4, v) were the overlarge sets of disjoint S(3, 4, 2 n ) obtained from the oval conics
A set of necessary conditions for the existence of a large set of t-designs, LS[N] (t, k, v), is N |( v&i k&i ) for i=0, 1, ..., t. We show that these conditions are sufficient for N=3, t=2, 3, or 4, and k 8.
An MTS(v) [or DTS(v)] is said to be resolvable, denoted by RMTS(v) [or RDTS(v)], if its block set can be partitioned into parallel classes. An MTS(v) [or DTS(v)] is said to be almost resolvable, denoted by ARMTS(v) [or ARDTS(v)], if its bloak set can be partitioned into almost parallel classes. The
## Abstract In this paper, we present three constructions for antiβmitre Steiner triple systems and a construction for 5βsparse ones. The first construction for antiβmitre STSs settles two of the four unsettled admissible residue classes modulo 18 and the second construction covers such a class mod