Further constructions of square integer relative Heffter arrays

Abstract

A square integer relative Heffter array is an $n\times n$ array whose rows and columns sum to zero, each row and each column has exactly $k$ entries and either $x$ or $-x$ appears in the array for every $x\in {\mathbb{Z}}_{2nk+t}\setminus J$, where $J$ is a subgroup of size $t$. There are many open problems regarding the existence of these arrays. In this paper we construct two new infinite families of these arrays with the additional property that they are strippable. These constructions complete the existence theory for square integer relative Heffter arrays in the case where $k=3$ and $n$ is prime.

12 pages, 2 figures V2: Correction to reference 5. Date changed from 2019 to 2020