Bibliographic Details
| Title: |
Heffter spaces. |
| Authors: |
Buratti, M.1 (AUTHOR) marco.buratti@uniroma1.it, Pasotti, A.1,2 (AUTHOR) anita.pasotti@unibs.it |
| Source: |
Finite Fields & Their Applications. Sep2024, Vol. 98, pN.PAG-N.PAG. 1p. |
| Subjects: |
Orthogonal systems, Vector spaces, Finite fields |
| Abstract: |
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 odd block size and arbitrarily large degree r obtained with the crucial use of finite fields. Among the applications we establish, in particular, that if q = 2 k w + 1 is a prime power with kw odd and k ≥ 3 , then there are at least ⌈ w 4 k 4 ⌉ mutually orthogonal k -cycle systems of order q. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
