Configurations and trades in Steiner triple systems
نویسندگان
چکیده
The main result of this paper is the determination of all pairwise nonisomorphic trade sets of volume at most 10 which can appear in Steiner triple systems. We also enumerate partial Steiner triple systems having at most 10 blocks as well as configurations with no points of degree 1 and tradeable configurations having at most 12 blocks.
منابع مشابه
On the spectrum of simple (v, 3, 2) trades
In this paper, we determine the spectrum (the set of all possible volumes) of simple (v, 3, 2) trades for any fixed foundation size v 6≡ 5 (mod 6). Index Words: trades, spectrum, Steiner triple systems, large sets of Steiner triple systems MR Subject Classification: 05B07, 05B05
متن کاملCharacterization of affine Steiner triple systems and Hall triple systems
It is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration C14. We find three configurations such that a Steiner Electronic Notes in Discrete Mathematics 29 (2007) 17–21 1571-0653/$ – see front matter © 2007 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm doi:10.1016/j.endm.2007.07.004 triple system is affine if and on...
متن کاملOn 2-(v, 3) trades of minimum volume
In this paper, Steiner and non-Steiner 2-(v, 3) trades of minimum volume are considered. It is shown that these trades are composed of a union of some Pasch configurations and possibly some 2-(v, 3) trades with 6 ≤ v ≤ 10. We determine the number of non-isomorphic Steiner 2-(v, 3) trades of minimum volume. As for non-Steiner trades the same thing is done for all vs, except for v ≡ 5 (mod 6).
متن کامل5-sparse Steiner Triple Systems of Order n Exist for Almost All Admissible n
Steiner triple systems are known to exist for orders n ≡ 1, 3 mod 6, the admissible orders. There are many known constructions for infinite classes of Steiner triple systems. However, Steiner triple systems that lack prescribed configurations are harder to find. This paper gives a proof that the spectrum of orders of 5-sparse Steiner triple systems has arithmetic density 1 as compared to the ad...
متن کاملSteiner Trades That Give Rise to Completely Decomposable Latin Interchanges
In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges. 1 Background information In any combinatorial configuration it is possible to identify a subset which uniquely determines the structure of the configuration and in some cases i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 29 شماره
صفحات -
تاریخ انتشار 2004