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Book spreads in PG (7, 2)

Shaw, Ronald; Topalova, Svetlana T.

Authors

Ronald Shaw

Svetlana T. Topalova



Abstract

An (n,q,r,s) book is a collection of r-subspaces in PG(n,q) called pages, which cover the whole projective space and intersect in a common s-subspace called the spine such that any point outside the spine is in exactly one page. An (n,q,r,s) book t-spread is a t-spread in PG(n,q) for which there exists an (n,q,r,s) book, such that the points of each page of this book and hence the points of the spine are partitioned by t-subspaces of the t-spread. We commence by showing that an (n,q,r,s)book t-spread exists if and only if the following three conditions hold: (i) (r-s)|(n-s),(ii) (t+1)|(s+1),(iii) (t+1)|(r+1). In general the number of different kinds of (n,q,r,s) book t-spreads is a tiny proportion of the number of different kinds of t-spreads in PG(n,q). In the rest of this paper we present computer-aided classification results for certain types of (7,2,5,3) book 1-spreads. © 2014 Published by Elsevier B.V.

Journal Article Type Article
Publication Date Sep 6, 2014
Journal Discrete Mathematics
Print ISSN 0012-365X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 330
Pages 76-86
APA6 Citation Shaw, R., & Topalova, S. T. (2014). Book spreads in PG (7, 2). Discrete Mathematics, 330, 76-86. doi:10.1016/j.disc.2014.04.013
DOI https://doi.org/10.1016/j.disc.2014.04.013
Keywords Projective space; Book spread; Existence; Classification
Publisher URL https://www.sciencedirect.com/science/article/pii/S0012365X14001538?via%3Dihub
Additional Information This article is maintained by: Elsevier; Article Title: Book spreads in; Journal Title: Discrete Mathematics; CrossRef DOI link to publisher maintained version: http://dx.doi.org/10.1016/j.disc.2014.04.013; Content Type: article; Copyright: Copyright © 2014 Elsevier B.V. All rights reserved.


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