On the sum of dilations of a set
Acta Arithmetica (2014)
- Volume: 164, Issue: 2, page 153-162
- ISSN: 0065-1036
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topAntal Balog, and George Shakan. "On the sum of dilations of a set." Acta Arithmetica 164.2 (2014): 153-162. <http://eudml.org/doc/279398>.
@article{AntalBalog2014,
abstract = {We show that for any relatively prime integers 1 ≤ p < q and for any finite A ⊂ ℤ one has $|p·A + q·A| ≥ (p+q)|A| - (pq)^\{(p+q-3)(p+q)+1\}$.},
author = {Antal Balog, George Shakan},
journal = {Acta Arithmetica},
keywords = {additive combinatorics; sumset estimates},
language = {eng},
number = {2},
pages = {153-162},
title = {On the sum of dilations of a set},
url = {http://eudml.org/doc/279398},
volume = {164},
year = {2014},
}
TY - JOUR
AU - Antal Balog
AU - George Shakan
TI - On the sum of dilations of a set
JO - Acta Arithmetica
PY - 2014
VL - 164
IS - 2
SP - 153
EP - 162
AB - We show that for any relatively prime integers 1 ≤ p < q and for any finite A ⊂ ℤ one has $|p·A + q·A| ≥ (p+q)|A| - (pq)^{(p+q-3)(p+q)+1}$.
LA - eng
KW - additive combinatorics; sumset estimates
UR - http://eudml.org/doc/279398
ER -
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