Journal article
Contractions and expansion
- Abstract:
- Let A be a finite set of reals and let K >= 1 be a real number. Suppose that for each a in A we are given an injective map f_a : A -> R which fixes a and contracts other points towards it in the sense that |a - f_a(x)| <= |a - x|/K for all x in A, and such that f_a(x) always lies between a and x. Then the union of the f_a(A) has cardinality >= K|A|/10 - O_K(1). An immediate consequence of this is the estimate |A + K.A| >= K|A|/10 - O_K(1), which is a slightly weakened version of a result of Bukh.
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Bibliographic Details
- Publication date:
- 2011-12-15
- Source identifiers:
-
398459
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Terms of use
- Copyright date:
- 2011
- Notes:
-
6 pages, submitted to special volume of EJC in honour of Yahya
Hamidoune
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