The Number of Homothetic Subsets

Miklós Laczkovich () and Imre Z. Ruzsa ()
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Miklós Laczkovich: Eötvös Loránd University, Department of Analysis
Imre Z. Ruzsa: Mathematical Institute of the Hungarian Academy of Sciences

A chapter in The Mathematics of Paul Erdős I, 2013, pp 523-532 from Springer

Abstract: Summary We investigate the maximal number S(P, n) of subsets of a set of n elements homothetic to a fixed set P. Elekes and Erdős proved that S(P, n) > cn 2 if | P | = 3 or the elements of P are algebraic. For | P | ≥ 4 we show that S(P, n) > cn 2 if and only if every quadruple in P has an algebraic cross ratio. Moreover, there is a sequence S n of numbers such that $$S(P,n) \asymp S_{n}$$ whenever | P | = 4 and the cross ratio of P is transcendental.

Keywords: primary 52ClO; secondary 05D99 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-7258-2_32

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DOI: 10.1007/978-1-4614-7258-2_32

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