Let $H^{(3)}$ be a uniform hypergraph of rank 3. A $3$-\emph{helix} $S^{(3)}(1,3)$ of \emph{centre} $\{c\}$ is a {3-uniform} hypergraph, with 3 hyperedges, all having in common exactly the \emph{centre} $\{c\}$, with $c$ of degree 3 and the remaining vertices of degree 1. In this paper we determine the spectrum of {$S^{(3)}(1,3)$-\emph{designs}}, for every index $\lambda$.
Construction of 3-helix systems of any index
Causa Antonio;Gionfriddo Mario;Guardo Elena
2024-01-01
Abstract
Let $H^{(3)}$ be a uniform hypergraph of rank 3. A $3$-\emph{helix} $S^{(3)}(1,3)$ of \emph{centre} $\{c\}$ is a {3-uniform} hypergraph, with 3 hyperedges, all having in common exactly the \emph{centre} $\{c\}$, with $c$ of degree 3 and the remaining vertices of degree 1. In this paper we determine the spectrum of {$S^{(3)}(1,3)$-\emph{designs}}, for every index $\lambda$.File in questo prodotto:
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