2024/01/08 by Buratti, Marco, Pasotti, Anita · 3 citations
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2401.03940
The notion of a Heffter array, which received much attention in the last decade, is equivalent to a pair of orthogonal Heffter systems. In this paper we study the existence problem of a set of r mutually orthogonal Heffter systems for any r. Such a set is equivalent to a resolvable partial linear space of degree r whose parallel classes are Heffter systems: this is a new combinatorial design that we call a Heffter space. We present a series of direct constructions of Heffter spaces with block size odd and arbitrarily large degree r obtained with the crucial use of finite fields. Among the applications we establish, in particular, the existence of r mutually orthogonal k-cycle systems of order a prime power q=2kw+1 whenever kw is odd and w>4k4\lceilr\over k\rceil.