Partition relation
= Partition relation
{title2=$\lambda\rightarrow(\mu)^\alpha_\beta$}
The notation $\lambda\rightarrow(\mu)^\alpha_\beta$ says that every $\beta$-coloring of the $\alpha$-element subsets of $\lambda$ has a homogeneous subset of order type $\mu$. At infinite arity one specifies whether the domain subsets have a fixed cardinality or a fixed order type; the usual finite-arity notation has no such ambiguity.