Article
Version 1
Preserved in Portico This version is not peer-reviewed
Discovering Doily in PG(2,5)
Version 1
: Received: 17 April 2023 / Approved: 17 April 2023 / Online: 17 April 2023 (10:42:11 CEST)
A peer-reviewed article of this Preprint also exists.
Innamorati, S. Note on Discovering Doily in PG(2,5). Mathematics 2023, 11, 2210. Innamorati, S. Note on Discovering Doily in PG(2,5). Mathematics 2023, 11, 2210.
Abstract
W. L. Edge proved that the internal points of a conic in PG(2,5), together with the collinear triples on the non-secant lines, form the Desargues configuration. M. Saniga showed an intimate connection between Desargues configurations and the generalized quadrangles of order two, GQ(2,2), whose representation has been dubbed “the doily” by Stan Payne in 1973. In this paper we prove that the external points of a conic in PG(2,5), together with the collinear and non-collinear triples on the non-tangent lines, form the generalized quadrangle of order two.
Keywords
Desargues configuration; Generalized quadrangle of order two; Projective plane of order five
Subject
Computer Science and Mathematics, Discrete Mathematics and Combinatorics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
