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July 26, 2026Open Access

The Exact Minimum Order for Unique Multiset Sums in Finite Abelian Groups

Key Points

The aim is to establish the exact minimum order for unique multiset sums in finite abelian groups and classify all equality cases.
Proved the sharp bound of 2^{n-1} for unique multiset sums.
Classified all equality cases related to this bound.
Derived consequences for finite-abelian character schemes.
Established the minimum order as 2^{n-1}.
Classified all equality cases successfully.
Derived insights into character schemes used in permanent evaluation.

Abstract

This project presents a proof of the exact minimum order for unique multiset sums in finite abelian groups, resolving an open problem posed by J. A. R. Fonollosa. It establishes the sharp bound 2^n-1, classifies all equality cases, and derives a consequence for finite-abelian character schemes used in permanent evaluation.

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Michael Behzat Ali Inal (Fri,) studied this question.

synapsesocial.com/papers/6a65a8c9d3aea3239cd78f80 https://doi.org/https://doi.org/10.17605/osf.io/c58q9