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Title: Some remarks on the Erdős Distinct subset sums problem
Let [Formula: see text] be a set of positive integers, [Formula: see text] denoting the largest element, so that for any two of the [Formula: see text] subsets the sum of all elements is distinct. Erdős asked whether this implies [Formula: see text] for some universal [Formula: see text]. We prove, slightly extending a result of Elkies, that for any [Formula: see text], [Formula: see text] with equality if and only if all subset sums are [Formula: see text]-separated. This leads to a new proof of the currently best lower bound [Formula: see text]. The main new insight is that having distinct subset sums and [Formula: see text] small requires the random variable [Formula: see text] to be close to Gaussian in a precise sense.  more » « less
Award ID(s):
2123224
PAR ID:
10528280
Author(s) / Creator(s):
Publisher / Repository:
World Scientific Publishing
Date Published:
Journal Name:
International Journal of Number Theory
Volume:
19
Issue:
08
ISSN:
1793-0421
Page Range / eLocation ID:
1783 to 1800
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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