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 >= 3 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.
More Heffter Spaces via Finite Fields
Buratti M.;Pasotti A.
2025-01-01
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 >= 3 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.File in questo prodotto:
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