On the number of k-rich transformations

Authors:
Jozsef Solymosi;Gabor Tardos
Affiliations:
University of British Columbia, Vancouver, BC, Canada;Simon Fraser University, Burnaby, BC, Canada
Venue:
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Year:
2007

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Structural Results For Planar Sets With Many Similar Subsets

Combinatorica

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Abstract

Given a finite set of complex numbers A we say that a transformation on the complex numbers, T: C → C is k-rich on A if |A ∩ T(A)|≥ k. In this paper we give a bounds on the number of k-rich linear and Möbius transformations for any given set A. Our results have applications to discrete geometry and to additive combinatorics.