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The correlations of finite Desarguesian planes of square order defined by diagonal matrices

โœ Scribed by Barbu C. Kestenband

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
233 KB
Volume
423
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

The present article represents the next step in our ongoing program of classifying the correlations of finite Desarguesian planes.

We show that in PG(2, q 2n ), the correlations defined by diagonal matrices, with companion automorphism (q m ), where (m, 2n) = 1, have the following numbers of absolute points: q 2n + q n+2q n+1 + 1 or q 2nq n+1 + q n + 1 or (q n + 1) 2 for n odd; q 2nq n+2 + q n+1 + 1 or q 2n + q n+1q n + 1 or (q n -1) 2 for n even.

We also discuss the equivalence classes into which these correlations fall, as well as the configurations of their sets of absolute points.

๐Ÿ“œ SIMILAR VOLUMES

The correlations with identity companion
The correlations with identity companion automorphism, of finite Desarguesian planes
โœ Barbu C. Kestenband ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 176 KB

As a first step towards the general classification of correlations of finite Desarguesian planes, we present, up to isomorphism, all the correlations with identity companion automorphism which are not polarities, of such planes.

A three-class association scheme on the
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โœ I.M. Chakravarti ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 262 KB

First we define relations between the u = (s\* + s + 1) (s + 1) flags (point-line incident pairs) of a finite projective plane of order s. Two flags a E (p, 1) and b = (p', l'), where p and p' are two points and 1 and 1' are two lines of the projective plane, are defined to