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 \(\sum_{i\in J}d_i \geq \binom{|J|}{2}\) for all \(J\subseteq \{1,2,\dots, n\}\), with equality if \(|J|=n\). Moon \cite{Moon63} extended this result to generalised t...

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Bibliographic Details
Published in:arXiv.org 2016-07
Main Author: Thörnblad, Erik
Format: Article
Language:English
Subjects:
Integers
Tournaments & championships
Online Access:Get full text
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Summary: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.
ISSN:2331-8422