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Embedding the complement of an oval in a projective plane of even order

✍ Scribed by R.C. Bose; S.S. Shrikhande

Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
729 KB
Volume
6
Category
Article
ISSN
0012-365X

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✦ Synopsis

A configuration D with parameters (u, b, r. k) is an incidence structure t P, B. 2 L where ? is a set of u "points'*, 8 is a set of b '"blocks" and 7 is an 'incidence relation" between points and blocks such that each point is incident with t blocks, and each blok is incident with Fc points. A block may be regarded ac. the subset of those points of p with which it is incident.

A regular two component pairwise balanced design with parameters 1. I. A configuration I? with parameters (v, b, I' k) is an insidTnee structure (P, 8, I), where P is a set of u "points". 6 is a set of b 'Wocks"

πŸ“œ SIMILAR VOLUMES

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A blocking set B in a projective plane z of order n is a subset of T which meets every line but contains no line completely. Hence le)B n I] srz for every line i of 9r.I A blocking set is minimal if it contains no proper blocking set. A blocking set is maximal if it is not properly contained in any

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This paper reports the result of a computer search which show s that there is no oval in a projective plane of order 10. It gives a brief description of the search method as well as a brief survey of other possible configurations in a plane of order 10.

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Let be a projective plane of odd order n containing an oval ⍀. We give a classification of collineation groups of which fix ⍀ and act transitively on the set I I of all internal points of ⍀.

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We show how to lift the even intersection equivalence relation from the hyperovals of PG(2, 4) to an equivalence relation amongst sets of hyperconics in "PG(2, F ). Here, F is any "nite or in"nite "eld of characteristic two that contains a sub"eld of order 4, but does not contain a sub"eld of order