Symmetric set function
= Symmetric set function
{title2=$f(S)=f(V\setminus S)$}
A <set function> on the <power set> of a <ground set> $V$ is symmetric when complementary <subsets> have equal values. A <hypergraph cut function> has this property because swapping the two sides changes no crossing <hyperedge>. If a <symmetric set function> is also a <monotone set function>, it is constant: $f(\varnothing)\leq f(S)\leq f(V)=f(\varnothing)$.