✦ LIBER ✦

Self-embeddings of cyclic and projective Steiner quasigroups

✍ Scribed by Diane M. Donovan; Mike J. Grannell; Terry S. Griggs; James G. Lefevre; Thomas McCourt

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 138 KB
Volume: 19
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20258

No coin nor oath required. For personal study only.

✦ Synopsis

It is shown that for every admissible order v for which a cyclic Steiner triple system exists, there exists a biembedding of a cyclic Steiner quasigroup of order v with a copy of itself. Furthermore, it is shown that for each n ≥ 2 the projective Steiner quasigroup of order 2 n -1 has a biembedding with a copy of itself.

📜 SIMILAR VOLUMES

Cyclic projective planes and binary, ext

Cyclic projective planes and binary, extended cyclic self-dual codes

✍ Vera Pless 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 144 KB

Cyclic bi-embeddings of Steiner triple s

Cyclic bi-embeddings of Steiner triple systems on 12s + 7 points

✍ G. K. Bennett; M. J. Grannell; T. S. Griggs 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 196 KB 👁 1 views

## Abstract A cyclic face 2‐colourable triangulation of the complete graph __K__~__n__~ in an orientable surface exists for __n__ ≡ 7 (mod 12). Such a triangulation corresponds to a cyclic bi‐embedding of a pair of Steiner triple systems of order __n__, the triples being defined by the faces in eac

Unique and faithful embeddings of projec

Unique and faithful embeddings of projective-planar graphs

✍ Seiya Negami 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 393 KB

A graph G is uniquelyembeddable in a surface f 2 if for any two embeddings f,,f2 : G + f 2 , there exists an isomorphism u : G + G and a homeo- admits an embedding f : G + F2 such that for any isomorphism (T : G + G, there is a homeomorphism h : F 2 f 2 with h . f = f . u. It will be shown that if

Surface embeddings of Steiner triple sys

Surface embeddings of Steiner triple systems

✍ M. J. Grannell; T. S. Griggs; Jozef S˘irán˘ 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 421 KB 👁 1 views

A Steiner triple system of order n (STS(n)) is said to be embeddable in an orientable surface if there is an orientable embedding of the complete graph Kn whose faces can be properly 2-colored (say, black and white) in such a way that all black faces are triangles and these are precisely the blocks

On projective embeddings of partial plan

On projective embeddings of partial planes and rank-three matroids

✍ Franz Kalhoff 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 543 KB

Any finite partial plane J, and thus any finite linear spa~e and any (simple) rank-three matroid, can be embedded into a translation plane. It even turns out, that o¢ is embeddable into a projective plane of Lenz class V, and that the characteristic of this plane can be chosen arbitrarily. In partic

Cyclic resolvability of cyclic Steiner 2

Cyclic resolvability of cyclic Steiner 2-designs

✍ Masaki Genma; Miwako Mishima; Masakazu Jimbo 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 163 KB

In this article, direct and recursive constructions for a cyclically resolvable cyclic Steiner 2-design are given.