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 (16ℓ2,4ℓ;3) Heffter space for any ℓ≥1. Combining these constructions we obtain a shiftable (16ℓ2mn,4ℓn;3) Heffter space for every triple of positive integers (ℓ,m,n) with m≥n.
Shiftable heffter spaces / Buratti, M.; Pasotti, A.. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - 93:9(2025), pp. 3863-3874. [10.1007/s10623-025-01657-1]
Shiftable heffter spaces
Buratti M.Primo
Writing – Original Draft Preparation
;
2025
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 (16ℓ2,4ℓ;3) Heffter space for any ℓ≥1. Combining these constructions we obtain a shiftable (16ℓ2mn,4ℓn;3) Heffter space for every triple of positive integers (ℓ,m,n) with m≥n.| File | Dimensione | Formato | |
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