Premium
Lacunary Polynomials, Multiple Blocking Sets and Baer Subplanes
Author(s) -
Blokhuis A.,
Storme L.,
Szőnyi T.
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007875
Subject(s) - lacunary function , mathematics , combinatorics , disjoint sets , projective line , generalization , polynomial , blocking set , disjoint union (topology) , discrete mathematics , point (geometry) , set (abstract data type) , square (algebra) , line (geometry) , pure mathematics , projective space , projective test , collineation , mathematical analysis , geometry , computer science , programming language
New lower bounds are given for the size of a point set in a Desarguesian projective plane over a finite field that contains at least a prescribed number s of points on every line. These bounds are best possible when q is square and s is small compared with q . In this case the smallest set is shown to be the union of disjoint Baer subplanes. The results are based on new results on the structure of certain lacunary polynomials, which can be regarded as a generalization of Rédei's results in the case when the derivative of the polynomial vanishes.