Contractions and expansion

Breuillard, E; Green, B

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

Email

Email this record

Send the bibliographic details of this record to your email address.

Your Email
Please enter the email address that the record information will be sent to.

Your message (optional)
Please add any additional information to be included within the email.
Cite

Cite this record

APA Style

Breuillard, E., & Green, B. (2011). Contractions and expansion.

MLA Style

Breuillard, E., and B. Green. Contractions and Expansion. 2011.

Chicago Style

Breuillard, E, and B Green. 2011. “Contractions and Expansion.”
Tweet
Print

Authors

Breuillard, E More by this author

Green, B More by this author

Bibliographic Details

Publication date:: 2011-12-15
URN:: uuid:879843c1-33c6-4eff-b6f5-5189a326d95c
Source identifiers:: 398459
Local pid:: pubs:398459

Item Description

Keywords:: math.CO

math.NT

Terms of use

Notes:: 6 pages, submitted to special volume of EJC in honour of Yahya
Hamidoune

License:: Terms and Conditions of Use for Oxford University Research Archive

Views & Downloads

Metrics

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