Equidistribution of subset sums

TL;DR

This paper proves that in large abelian groups, the sums of subsets of size half the group order become evenly distributed as the subset size grows, extending previous questions about distribution.

Contribution

It establishes asymptotic equidistribution of subset sums in abelian groups of arbitrary order, with explicit bounds on the error term.

Findings

Subset sums are asymptotically equidistributed in large abelian groups.

The result generalizes previous specific cases to arbitrary group orders.

Provides bounds for the deviation from perfect uniformity.

Abstract

We answer a question of Katona and Makar-Limanov, by showing that in an abelian group of order $2h$ the $h$-element subset sums are asymptotically (as $h\to \infty$) equidistributed. In fact we prove a more general result where the order of the group can be arbitrary, also providing a bound for the ``error term''.