### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 321-332 |

Number of pages | 12 |

Journal | Journal of the London Mathematical Society |

Volume | 60 |

Issue number | 2 |

Publication status | Published - Oct 1999 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the London Mathematical Society*,

*60*(2), 321-332.

**Lacunary polynomials, multiple blocking sets and baer subplanes.** / Blokhuis, A.; Storme, L.; Szőnyi, T.

Research output: Contribution to journal › Article

*Journal of the London Mathematical Society*, vol. 60, no. 2, pp. 321-332.

}

TY - JOUR

T1 - Lacunary polynomials, multiple blocking sets and baer subplanes

AU - Blokhuis, A.

AU - Storme, L.

AU - Szőnyi, T.

PY - 1999/10

Y1 - 1999/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0008596779&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0008596779&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0008596779

VL - 60

SP - 321

EP - 332

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 2

ER -