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Book spreads in PG (7, 2)

Shaw, Ronald; Topalova, Svetlana T.


Ronald Shaw

Svetlana T. Topalova


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.


Shaw, R., & Topalova, S. T. (2014). Book spreads in PG (7, 2). Discrete Mathematics, 330, 76-86.

Journal Article Type Article
Acceptance Date Apr 11, 2014
Online Publication Date May 4, 2014
Publication Date Sep 6, 2014
Deposit Date Jun 29, 2018
Journal Discrete Mathematics
Print ISSN 0012-365X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 330
Pages 76-86
Keywords Projective space; Book spread; Existence; Classification
Public URL
Publisher URL
Additional Information This article is maintained by: Elsevier; Article Title: Book spreads in; Journal Title: Discrete Mathematics; CrossRef DOI link to publisher maintained version:; Content Type: article; Copyright: Copyright © 2014 Elsevier B.V. All rights reserved.

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