Journal of Integer Sequences, Vol. 28 (2025), Article 25.7.8

Maximal Subset Sums in a Group of Order a Power of 2


John Greene and Clayton Higgins
Department of Mathematics and Statistics
University of Minnesota Duluth
Duluth, MN 55812
USA

Abstract:

If $G$ is an abelian group of order $2^{n}$, and $S = \{g_{1}, g_{2}, \ldots, g_{n} \}$ is a subset of $G$, we call $S$ a perfect cover for $G$ if every element of $G$ is the subset sum of elements in $S$. We prove that perfect covers always exist and count how many perfect covers there are for selected groups. In particular, we count the number of perfect covers for the groups $\mathbb{Z}_{2^{m}} \oplus \mathbb{Z}_{2^{n}}$ and $(\mathbb{Z}_{2})^{m} \oplus \mathbb{Z}_{2^{n}}$.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A006125 A053601 A123903.)

Received December 23 2024; revised versions received December 31 2024; February 11 2025; December 5 2025; December 8 2025. Published in Journal of Integer Sequences, December 10 2025.

Return to Journal of Integer Sequences home page