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

TL;DR

This paper demonstrates how Moon's theorem on generalized tournament score sequences can be derived from Landau's theorem, providing a new perspective on the relationship between these two fundamental results.

Contribution

It offers a novel proof of Moon's theorem by reducing it to Landau's theorem, clarifying the connection between the two results.

Findings

Moon's theorem can be derived from Landau's theorem

Provides a new proof technique for generalized tournament scores

Clarifies the relationship between Landau's and Moon's results

Abstract

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 $\sum_{i\in J}d_i \geq \binom{|J|}{2}$ for all $J\subseteq \{1,2,\dots, n\}$, with equality if $|J|=n$. Moon \cite{Moon63} extended this result to generalised tournaments. We show how Moon's result can be derived from Landau's result.