CORE
🇺🇦Â
 make metadata, not war
Services
Services overview
Explore all CORE services
Access to raw data
API
Dataset
FastSync
Content discovery
Recommender
Discovery
OAI identifiers
OAI Resolver
Managing content
Dashboard
Bespoke contracts
Consultancy services
Support us
Support us
Membership
Sponsorship
Community governance
Advisory Board
Board of supporters
Research network
About
About us
Our mission
Team
Blog
FAQs
Contact us
On Bruen chains
Authors
John Bamberg
Jesse Lansdown
Geertrui Van de Voorde
Publication date
2 May 2023
Publisher
View
on
arXiv
Abstract
It is known that a Bruen chain of the three-dimensional projective space
P
G
(
3
,
q
)
\mathrm{PG}(3,q)
PG
(
3
,
q
)
exists for every odd prime power
q
q
q
at most
37
37
37
, except for
q
=
29
q=29
q
=
29
. It was shown by Cardinali et. al (2005) that Bruen chains do not exist for
41
≤
q
≤
49
41\le q\leq 49
41
≤
q
≤
49
. We develop a model, based on finite fields, which allows us to extend this result to
41
⩽
q
⩽
97
41\leqslant q \leqslant 97
41
⩽
q
⩽
97
, thereby adding more evidence to the conjecture that Bruen chains do not exist for
q
>
37
q>37
q
>
37
. Furthermore, we show that Bruen chains can be realised precisely as the
(
q
+
1
)
/
2
(q+1)/2
(
q
+
1
)
/2
-cliques of a two related, yet distinct, undirected simple graphs
Similar works
Full text
Available Versions
arXiv.org e-Print Archive
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:arXiv.org:2305.01349
Last time updated on 06/05/2023