منابع مشابه
Extending Arcs: An Elementary Proof
In a finite projective plane π we consider two configuration conditions involving arcs in π and show via combinatorial means that they are equivalent. When the conditions hold we are able to obtain embeddability results for arcs, all proofs being elementary. In particular, when π = PG(2, q) with q even we provide short proofs of some well known embeddability results.
متن کاملNew Large (n, r)-arcs in PG(2, q)
An $(n, r)$-arc is a set of $n$ points of a projective plane such that some $r$, but no $r+1$ of them, are collinear. The maximum size of an $(n, r)$-arc in $PG(2, q)$ is denoted by $m_r(2,q)$. In this paper we present a new $(184,12)$-arc in PG$(2,17),$ a new $(244,14)$-arc and a new $(267,15$)-arc in $PG(2,19).$
متن کاملLarge 2-transitive arcs
The projective planes of order n with a collineation group acting 2-transitively on an arc of length v, with n > v n/2, are investigated and several new examples are provided. © 2006 Elsevier Inc. All rights reserved.
متن کاملExtending pseudo-arcs in odd characteristic
A pseudo-arc in PG(3n− 1, q) is a set of (n− 1)-spaces such that any three of them span the whole space. A pseudo-arc of size qn + 1 is a pseudo-oval. If a pseudo-oval O is obtained by applying field reduction to a conic in PG(2, qn), then O is called a pseudo-conic. We first explain the connection of (pseudo-)arcs with Laguerre planes, orthogonal arrays and generalised quadrangles. In particul...
متن کاملArcs with Large Conical Subsets
We classify the arcs in PG(2, q), q odd, which consist of (q + 3)/2 points of a conic C and two points not on te conic but external to C, or (q + 1)/2 points of C and two additional points, at least one of which is an internal point of C. We prove that for arcs of the latter type, the number of points internal to C can be at most 4, and we give a complete classification of all arcs that attain ...
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ژورنال
عنوان ژورنال: European Journal of Mathematics
سال: 2017
ISSN: 2199-675X,2199-6768
DOI: 10.1007/s40879-017-0193-x