Szczegóły publikacji
Opis bibliograficzny
Trinal decompositions of steiner triple systems into triangles / Charles C. Lindner, Mariusz MESZKA, Alexander Rosa // Journal of Combinatorial Designs ; ISSN 1063-8539. — 2013 — vol. 21 iss. 5, s. 204–211. — Bibliogr. s. 211, Abstr.
Autorzy (3)
- Lindner Charles C.
- AGHMeszka Mariusz
- Rosa Alexander
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 72559 |
|---|---|
| Data dodania do BaDAP | 2013-03-21 |
| Tekst źródłowy | URL |
| DOI | 10.1002/jcd.21319 |
| Rok publikacji | 2013 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Journal of Combinatorial Designs |
Abstract
It is well known that when n1 or 9(mod18), there exists a Steiner triple system (STS) of order n decomposable into triangles (three pairwise intersecting triples whose intersection is empty). A triangle {a,b,c},{c,d,e},{e,f,a} in an STS determines naturally two more triples: the triple of vertices {a,c,e}, and the triple of midpoints {b,d,f}. The number of these triples in both cases, that of vertex triples (inner) or that of midpoint triples (outer), equals one-third of the number of triples in the STS. In this paper, we consider a new problem of trinal decompositions of an STS into triangles. In this problem, one asks for three distinct decompositions of an STS of order n into triangles such that the union of the three collections of inner triples (outer triples, respectively) from the three decompositions form the set of triples of an STS of the same order. These decompositions are called trinal inner and trinal outer decompositions, respectively. We settle the existence question for trinal inner decompositions completely, and for trinal outer decompositions with two possible exceptions.
