Compact symmetric solutions to the postage stamp problem

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 $n\in \{0,1,2,...,k{a}_k\}$ can be represented as a sum of no more than $k$ elements of $A_k$, with repetition.

arXiv comment6 pages, final version to appear in FJMS