## Abstract This paper gives a proof of the existence of anti‐mitre Steiner triple systems of order __n__ for every __n__ ≡ 1,3 mod 6 except for __n__ = 9. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 229–236, 2006
Constructions for anti-mitre Steiner triple systems
✍ Scribed by Yuichiro Fujiwara
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 83 KB
- Volume
- 13
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
In this paper, we present a recursive construction for anti‐mitre Steiner triple systems. Furthermore, we present another construction of anti‐mitre STSs by utilizing 5‐sparse ones. © 2004 Wiley Periodicals, Inc.
📜 SIMILAR VOLUMES
## Abstract In this paper, we present three constructions for anti‐mitre Steiner triple systems and a construction for 5‐sparse ones. The first construction for anti‐mitre STSs settles two of the four unsettled admissible residue classes modulo 18 and the second construction covers such a class mod
## Abstract A direct construction for rotational Steiner quadruple systems of order __p__+ 1 having a nontrivial multiplier automorphism is presented, where __p__≡13 (mod24) is a prime. We also give two improved product constructions. By these constructions, the known existence results of rotationa
## Abstract The obvious necessary conditions for the existence of a nested Steiner triple system of order __v__ containing a nested subsystem of order __w__ are __v__ ≥ 3__w__ + 4 and __v__ ≡ w ≡ 1 (mod 6). We show that these conditions are also sufficient. © 2004 Wiley Periodicals, Inc.
## Abstract We explicitly construct four infinite families of irreducible triple systems with Ramsey‐Turán density less than the Turán density. Two of our families generalize isolated examples of Sidorenko 14, and the first author and Rödl 12. Our constructions also yield two infinite families of i
## Abstract In this note, the 80 non‐isomorphic triple systems on 15 points are revisited from the viewpoint of the convex hull of the characteristic vectors of their blocks. The main observation is that the numbers, of facets of these 80 polyhedra are all different, thus producing a new proof of t