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Keywords = generalized quadrangle of order two

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5 pages, 882 KB  
Article
Note on Discovering Doily in PG(2,5)
by Stefano Innamorati
Mathematics 2023, 11(9), 2210; https://doi.org/10.3390/math11092210 - 8 May 2023
Cited by 1 | Viewed by 1671
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 2, GQ(2,2), [...] Read more.
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 2, GQ(2,2), whose representation was dubbed “the doily” by Stan Payne in 1973. In this note, 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 2. Full article
(This article belongs to the Special Issue Discrete Mathematics, Graph Theory and Applications)
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5 pages, 374 KB  
Letter
Doily as Subgeometry of a Set of Nonunimodular Free Cyclic Submodules
by Metod Saniga and Edyta Bartnicka
Axioms 2019, 8(1), 28; https://doi.org/10.3390/axioms8010028 - 4 Mar 2019
Viewed by 3913
Abstract
In this paper, it is shown that there exists a particular associative ring with unity of order 16 such that the relations between non-unimodular free cyclic submodules of its two-dimensional free left module can be expressed in terms of the structure of the [...] Read more.
In this paper, it is shown that there exists a particular associative ring with unity of order 16 such that the relations between non-unimodular free cyclic submodules of its two-dimensional free left module can be expressed in terms of the structure of the generalized quadrangle of order two. Such a doily-centered geometric structure is surmised to be of relevance for quantum information. Full article
(This article belongs to the Special Issue Foundations of Quantum Computing)
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