منابع مشابه
On regular semiovals in PG(2, q)
In this paper we prove that a point set in PG(2, q) meeting every line in 0, 1 or r points and having a unique tangent at each of its points is either an oval or a unital. This answers a question of Blokhuis and Szőnyi [1].
متن کاملA survey on semiovals
A semioval in a finite projective plane is a non-empty pointset S with the property that for every point in S there exists a unique line tP such that S ∩ tP = {P}. This line is called the tangent to S at P . Semiovals arise in several parts of finite geometries: as absolute points of a polarity (ovals, unitals), as special minimal blocking sets (vertexless triangle), in connection with cryptogr...
متن کاملSome new results on small blocking semiovals
A blocking semioval S in a projective plane of order q is a set of points such that every line meets S in at least one point (the blocking property), and every point of S lies on a unique tangent line (the semioval property). The set of points on the sides of a triangle, excluding the vertices, is a blocking semioval in any projective plane of order q > 2, and has size 3q − 3. The size of a blo...
متن کاملFinite flag-transitive semiovals
A linear space is an incidence structure of points and lines such that any two points are incident with exactly one line, any point being incident with at least two lines and any line with at least two points. Within a linear space S, we shall often identify a line L with the set of points incident with L and define the size of L to be the number of points of S incident with L. The degree of a ...
متن کاملBlocking Semiovals of Type
We consider the existence of blocking semiovals in finite projective planes which have intersection sizes 1,m+ 1 or n+ 1 with the lines of the plane for 1 ≤ m < n. For those prime powers q ≤ 1024, in almost all cases, we are able to show that, apart from a trivial example, no such blocking semioval exists in a projective plane of order q. We are also able to prove, for general q, that if q2 + q...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2006
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-006-6029-2