Bi-embeddings of the projective space PG(3, 2)
type: Item
instance of: scholarly article
title: Bi-embeddings of the projective space PG(3, 2)
zbMATH Open document ID: 0958.05010
DOI: 10.1016/S0378-3758(99)00115-9
published in: Journal of Statistical Planning and Inference
publication date: 2000-09-18T00:00:00Z
review text: A bi-embedding of a pair of Steiner triple systems \(S\), \(S'\) in an (orientable or nonorientable) surface is a face 2-colourable triangulation of the surface in which the triangular faces of the two colours form Steiner triple systems isomorphic to \(S\) and \(S'\), respectively. The authors determine all bi-embeddings in which both \(S\) and \(S'\) are isomorphic to the design of points and lines of the projective space \(\text{PG}(3, 2)\). There is up to an isomorphism a unique bi-embedding in an orientable surface, and exactly three nonisomorphic bi-embeddings in a nonorientable surface.
Mathematics Subject Classification ID: 05B07
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 1471117
zbMATH Keywords: bi-embedding
zbMATH Keywords: Steiner triple systems
zbMATH Keywords: projective space
zbMATH Keywords: orientable surface
zbMATH Keywords: nonorientable surface
author: G. K. Bennett
author: Michael John Grannell
author: T. S. Griggs
reviewed by: Alexander Rosa
MaRDI profile type: Publication
cites work: Exponential families of non-isomorphic triangulations of complete graphs
cites work: Les G-Systemes Triples
cites work: Face 2-colourable triangular embeddings of complete graphs
cites work: Surface embeddings of Steiner triple systems
cites work: Q3663313
cites work: Q4773723
cites work: Nonisomorphic Steiner triple systems
cites work: Q5609151
full work available at URL: s0378-3758(99)00115-9
OpenAlex ID: W2159237067
description: scientific article; zbMATH DE number 1471117