Compact symmetric solutions to the postage stamp problem

TL;DR

This paper establishes bounds on the growth rates of specific integer sets that can represent all numbers up to a certain limit using limited summands, contributing to the understanding of the postage stamp problem.

Contribution

It provides new lower and upper bounds on the growth rates of sets solving the postage stamp problem with symmetric solutions.

Findings

Derived bounds on growth rates of integer sets

Applicable to the postage stamp problem

Enhances understanding of symmetric solutions

Abstract

We derive lower and upper bounds on possible growth rates of certain sets of positive integers $A_k=\{1= a_1 < a_2 < ... < a_{k}\}$ such that all integers $n\in \{0, 1, 2, ..., ka_{k}\}$ can be represented as a sum of no more than $k$ elements of $A_k$, with repetition.