Shiftable Heffter spaces

Abstract

The shiftable Heffter arrays are naturally generalized to the shiftable Heffter spaces. We present a recursive construction which starting from a single shiftable Heffter space leads to infinitely many other shiftable Heffter spaces of the same degree. We also present a direct construction making use of pandiagonal magic squares leading to a shiftable $(16{\ell }^2,4l;3)$ Heffter space for any $\ell \ge 1$. Combining these constructions we obtain a shiftable $(16{\ell }^{2}mn,4\ell n;3)$ Heffter space for every triple of positive integers $(\ell ,m,n)$ with $m\ge n$.