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Variations on the Erd\H{o}s distinct-sums problem
- Publication Year :
- 2021
-
Abstract
- Let $\{a_1, . . . , a_n\}$ be a set of positive integers with $a_1 < \dots < a_n$ such that all $2^n$ subset sums are distinct. A famous conjecture by Erd\H{o}s states that $a_n>c\cdot 2^n$ for some constant $c$, while the best result known to date is of the form $a_n>c\cdot 2^n/\sqrt{n}$. In this paper, we weaken the condition by requiring that only sums corresponding to subsets of size smaller than or equal to $\lambda n$ be distinct. For this case, we derive lower and upper bounds on the smallest possible value of $a_n$.
- Subjects :
- Mathematics - Combinatorics
Mathematics - Number Theory
05D40, 11B13
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2107.07885
- Document Type :
- Working Paper