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More Heffter Spaces via Finite Fields

A ( v , k ; r ) Heffter space is a resolvable ( v r , b k ) configuration whose points form a half‐set of an abelian group… Click to show full 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.

Keywords: finite fields; heffter; spaces via; via finite; group; heffter spaces

Journal Title: Journal of Combinatorial Designs
Year Published: 2024

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