Journal article icon

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.

Actions


Authors


Breuillard, E More by this author
Publication date:
2011-12-15
URN:
uuid:879843c1-33c6-4eff-b6f5-5189a326d95c
Source identifiers:
398459
Local pid:
pubs:398459
Keywords:

Terms of use


Metrics



If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP