EN
A hypergraph 𝓗 is a sum hypergraph iff there are a finite S ⊆ IN⁺ and d̲, [d̅] ∈ IN⁺ with 1 < d̲ ≤ [d̅] such that 𝓗 is isomorphic to the hypergraph $𝓗_{d̲,[d̅]} (S) = (V,𝓔)$ where V = S and $𝓔 = {e ⊆ S:d̲ ≤ |e| ≤ [d̅] ∧ ∑_{v∈ e} v ∈ S}$. For an arbitrary hypergraph 𝓗 the sum number σ = σ(𝓗) is defined to be the minimum number of isolated vertices $y₁,..., y_σ ∉ V$ such that $𝓗 ∪ {y₁,...,y_σ}$ is a sum hypergraph.
Generalizing the graph Cₙ we obtain d-uniform hypergraphs where any d consecutive vertices of Cₙ form an edge. We determine sum numbers and investigate properties of sum labellings for this class of cycle hypergraphs.