Counting Admissible Sets of Integers: A Proof of the Erdős--Nicolas--Sárközy Conjecture

A finite set of positive integers is admissible if any two of its subsets with the same sum have the same cardinality. In 1991, Erdős, Nicolas and Sárközy conjectured that $\log a(N)\asymp\sqrt N$, where $a(N)$ denotes the number of nonempty admissible subsets of $\{1,\ldots,N\}$. We prove this conj