More Heffter Spaces via finite fields

TL;DR

This paper extends the existence results of Heffter spaces by relaxing symmetry conditions, demonstrating that such configurations exist for a broader range of parameters using finite fields.

Contribution

It introduces a new approach using point-semiregular automorphism groups to prove the existence of Heffter spaces for even k, expanding previous results.

Findings

Existence of infinitely many Heffter spaces for various parameters.

Extension of results to cases with even k.

Use of finite fields in construction methods.

Abstract

A $(v,k;r)$ Heffter space is a resolvable $(v_r,b_k)$ configuration whose points form a half-set of an abelian group $G$ and whose blocks are all zero-sum in $G$. It was recently proved that there are infinitely many orders $v$ for which, given any pair $(k,r)$ with $k\geq3$ odd, a $(v,k;r)$ Heffter space exists. This was obtained by imposing a point-regular automorphism group. Here we relax this request by asking for a point-semiregular automorphism group. In this way the above result is extended also to the case $k$ even.