The subset sum problem for finite abelian groups

TL;DR

This paper provides a character-theoretic proof of formulas for counting subsets of finite abelian groups with specified sums, extending previous results to subsets excluding the identity element.

Contribution

It offers a concise proof of known formulas for subset sums in finite abelian groups and generalizes results to subsets not containing the identity element.

Findings

Derived formulas for subset sum counts using character theory

Extended previous results to subsets excluding the identity element

Provided a simplified proof for existing formulas

Abstract

Let G be a finite abelian group. For g in G and i an integer we define N(i,g) to be the number of subsets of G of size i which sum up to g. We will give a short proof, using character theory, of a formula for these N(i,g) due to Li and Wan. We also give a formula for N(i,g)*, the number of subsets of G not containing 0 of size i which sum up to g. This generalizes another result of Wan.