Flocks of cones of higher degree
type: Item
instance of: scholarly article
title: Flocks of cones of higher degree
zbMATH Open document ID: 1112.51001
author: Peter Sziklai
published in: Journal of Algebraic Combinatorics
publication date: 2007-03-16T00:00:00Z
review text: A flock of a cone of PG\((3,q)\) is a partition of the points of the cone different from the vertex into \(q\) disjoint plane sections. The author considers in PG\((3,q)\) for \( q>19 \) and for \(2\leq {d}\leq q^{1/6}\) the cone \(C=\{(1,t,t^d,z): t,z\in \text{GF}(q)\} \cup\{(0,0,1,z):z\in \text{GF}(q)\}\cup\{(0,0,0,1)\}\) and assumes that the planes \(E_i\), \(i=1,\dots,q-\varepsilon, (0,0,0,1)\notin\{E_i\}\), intersect \(C\setminus\{(0,0,0,1)\}\) in pairwise disjoint curves. The author proves that, if \(\varepsilon < [1/d^2q^{1/2}]\), then one can find additional \( \varepsilon\) planes (in a unique way), which extend \(E_i\) to a flock. The paper is based on an earlier paper of the author [J. Comb. Theory, Ser. A 113, No. 4, 698--702 (2006; Zbl 1097.51005)].
reviewed by: Jan Kurek
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 5134520
zbMATH Keywords: flock
zbMATH Keywords: cone
MaRDI profile type: Publication
full work available at URL: s10801-006-0036-1
OpenAlex ID: W2072578412
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DOI: 10.1007/S10801-006-0036-1
description: scientific article; zbMATH DE number 5134520