We consider the question when a set in a vector space over the rationals, with no differences occurring more than twice, is the union of countably many sets, none containing a difference twice. The answer is “yes” if the set is of size at most , “not” if the set is allowed to be of size . It is consistent that the continuum is large, but the statement still holds for every set smaller than continuum.
@article{bwmeta1.element.bwnjournal-article-cmv64i1p129bwm,
author = {P\'eter Komj\'ath},
title = {Vector sets with no repeated differences},
journal = {Colloquium Mathematicae},
volume = {66},
year = {1993},
pages = {129-134},
zbl = {0830.03020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv64i1p129bwm}
}
Komjáth, Péter. Vector sets with no repeated differences. Colloquium Mathematicae, Tome 66 (1993) pp. 129-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv64i1p129bwm/
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