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An alternative way to generalise the pentagon
Universitat Polit├Ęcnica de Catalunya, Barcelona, Spain.
The University of Western Australia, Crawley, WA, Australia.
The University of Western Australia, Crawley, WA, Australia.
Universitat Rovira i Virgili, Tarragona, Spain.
2013 (English)In: Journal of combinatorial designs (Print), ISSN 1063-8539, E-ISSN 1520-6610, Vol. 21, no 4, p. 163-179Article in journal (Refereed) Published
Abstract [en]

We introduce the concept of a pentagonal geometry as a generalization of the pentagon and the Desargues configuration, in the same vein that the generalized polygons share the fundamental properties of ordinary polygons. In short, a pentagonal geometry is a regular partial linear space in which for all points x, the points not collinear with the point x, form a line. We compute bounds on their parameters, give some constructions, obtain some nonexistence results for seemingly feasible parameters and suggest a cryptographic application related to identifying codes of partial linear spaces.

Place, publisher, year, edition, pages
John Wiley & Sons, 2013. Vol. 21, no 4, p. 163-179
Keywords [en]
generalized pentagon, generalized polygon, partial linear space, combinatorial configuration, distance regular graph
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-91459DOI: 10.1002/jcd.21325OAI: oai:DiVA.org:liu-91459DiVA, id: diva2:617995
Available from: 2013-04-25 Created: 2013-04-25 Last updated: 2017-12-06

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