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UNIONS OF LINES IN $F^{n}$

Part of: Harmonic analysis in several variables Discrete geometry

Published online by Cambridge University Press:  11 April 2016

Richard Oberlin
Richard Oberlin*
Affiliation:
Department of Mathematics, Florida State University, 208 Love Building, 1017 Academic way, Tallahassee, FL 32306, U.S.A. email richard.oberlin@gmail.com
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Abstract

We show that if a collection of lines in a vector space over a finite field has “dimension” at least $2(d-1)+\unicode[STIX]{x1D6FD}$ , then its union has “dimension” at least $d+\unicode[STIX]{x1D6FD}$ . This is the sharp estimate of its type when no structural assumptions are placed on the collection of lines. We also consider some refinements and extensions of the main result, including estimates for unions of $k$ -planes.

MSC classification

Primary: 42B25: Maximal functions, Littlewood-Paley theory 52C17: Packing and covering in $n$ dimensions

Information

Type
Research Article
Information
Mathematika , Volume 62 , Issue 3 , 2016 , pp. 738 - 752
Copyright
Copyright © University College London 2016 

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