The Davenport constant of an interval: a proof that $\mathsf{D}=\chi$

Abstract

For two positive integers $m$ and $M$, we study the Davenport constant of the interval of integers $[[-m,M]]$, that is the maximal length of a minimal zero-sum sequence composed of elements from $[[-m,M]]$. We prove the conjecture that it is equal to $m+M-r$ where $r$ is the smallest integer which can be decomposed as a sum of two non-negative integers $t_1$ and $t_2$ ($r=t_1+t_2$) having the property that $\gcd (M-t_1,m-t_2)=1$.

33 pages