A construction for sets of integers with distinct subset sums
type: Item
instance of: scholarly article
title: A construction for sets of integers with distinct subset sums
zbMATH Open document ID: 0932.11015
author: Tom Bohman
published in: The Electronic Journal of Combinatorics
publication date: 1998-02-18T00:00:00Z
full work available at URL: https://eudml.org/doc/120147
full work available at URL: v5i1r3.html
review text: Summary: A set \(S\) of positive integers has distinct subset sums if there are \(2^{|S|}\) distinct elements of the set \(\{ \sum_{x \in X} x: X \subset S\}\). Let \((f(n) = \min\{ \max S: |S|=n \) and \(S\) has distinct subset sums\}. Erdős conjectured \(f(n) \geq c2^{n}\) 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 \(f(n)\).
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 05D10
zbMATH DE Number: 1119068
zbMATH Keywords: distinct subset sums
zbMATH Keywords: upper bound
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1119068