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On sets of points with few odd secants

Part of: Finite geometry and special incidence structures

Published online by Cambridge University Press:  10 October 2019

Simeon Ball  and
Bence Csajbók
Simeon Ball*
Affiliation:
Departament de Matemàtiques, Universitat Politècnica de Catalunya, Mòdul C3, Campus Nord, c/ Jordi Girona 1–3, 08034 Barcelona, Spain
Bence Csajbók
Affiliation:
MTA–ELTE Geometric and Algebraic Combinatorics Research Group, ELTE Eötvös Loránd University, Budapest, Hungary, Department of Geometry, 1117 Budapest, Pázmány P. stny. 1/C, Hungary
*
*Corresponding author. Email: simeon@ma4.upc.edu
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Abstract

We prove that, for q odd, a set of q + 2 points in the projective plane over the field with q elements has at least 2q − c odd secants, where c is a constant and an odd secant is a line incident with an odd number of points of the set.

MSC classification

Primary: 51E20: Combinatorial structures in finite projective spaces
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 29 , Issue 1 , January 2020 , pp. 31 - 43
Copyright
© Cambridge University Press 2019 

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Footnotes

†

The first author acknowledges the support of project MTM2017-82166-P of the Spanish Ministerio de Economía y Competitividad.

‡

The second author is supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. The second author acknowledges the support of OTKA grant K 124950.

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