Geodesic
A construction for sets of integers with distinct subset sums
The electronic journal of combinatorics, Tome 5 (1998)
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A set S of positive integers has distinct subset sums if there are $2^{|S|}$ distinct elements of the set $\left\{ \sum_{x \in X} x: X \subset S \right\} . $ Let $$f(n) = \min\{ \max S: |S|=n {\rm \hskip2mm and \hskip2mm} S {\rm \hskip2mm has \hskip2mm distinct \hskip2mm subset \hskip2mm sums}\}.$$ Erdős conjectured $ f(n) \ge c2^{n}$ for some constant c. We give a construction that yields $f(n) < 0.22002 \cdot 2^{n}$ for n sufficiently large. This now stands as the best known upper bound on $ f(n).$
DOI : 10.37236/1341
Classification : 11B83, 11B75, 05D10
Mots-clés : distinct subset sums, upper bound 
@article{10_37236_1341,
     author = {Tom Bohman},
     title = {A construction for sets of integers with distinct subset sums},
     journal = {The electronic journal of combinatorics},
     year = {1998},
     volume = {5},
     doi = {10.37236/1341},
     zbl = {0932.11015},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1341/}
}
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Tom Bohman. A construction for sets of integers with distinct subset sums. The electronic journal of combinatorics, Tome 5 (1998). doi: 10.37236/1341

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