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Projecting Difference Sets on the Positive Orthant

Published online by Cambridge University Press:  01 September 2008

RON HOLZMAN ,
VSEVOLOD F. LEV  and
ROM PINCHASI
RON HOLZMAN
Affiliation:
Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel (e-mail: holzman@techunix.technion.ac.il, room@math.technion.ac.il)
VSEVOLOD F. LEV
Affiliation:
Department of Mathematics, The University of Haifa at Oranim, Tivon 36006, Israel (e-mail: seva@math.haifa.ac.il)
ROM PINCHASI
Affiliation:
Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel (e-mail: holzman@techunix.technion.ac.il, room@math.technion.ac.il)
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Abstract

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Let n ≥ 1 be an integer. Given a vector a=(a1,. . ,an)∈$\R^n$, write$$ \a^+:=(\max\{a_1,0\}\longc \max\{a_n,0\}) $$(the ‘projection of a onto the positive orthant’). For a set A⊆$\R^n$ put A+:={a+: a ∈ A} and A−A:={a−b: a, b ∈ A}. Improving previously known bounds, we show that |(A−A)+| ≥ |A|3/5/6 for any finite set A⊆$\R^3$, and that |(A−A)+| ≥ c|A|6/11/(log |A|)2/11 with an absolute constant c>0 for any finite set A⊆$R^4$ such that |A| ≥ 2.

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 5 , September 2008 , pp. 681 - 688
Copyright
Copyright © Cambridge University Press 2008

References

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