Another proof of Moon's theorem on generalised tournament score sequences

Landau \cite{Landau1953} showed that a sequence $(d_i{)}_{i=1}^n$ of integers is the score sequence of some tournament if and only if $\sum_{i\in J}d_i \geq \binom{|J|}{2}$forall$J\subseteq {1,2,\dots, n}$,withequalityif$|J|=n$. Moon \cite{Moon63} extended this result to generalised tournaments. We show how Moon’s result can be derived from Landau’s result.