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Balanced Non-Transitive Dice II: Tournaments
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abstract
We further study sets of labeled dice in which the relation "is a better die than" is non-transitive. Focusing on sets with an additional symmetry we call "balance," we prove that sets of $n$ such $m$-sided dice exist for all $n,m \geq 3$. We then show how to construct a set of $n$ dice such that the relation behaves according to the direction of the arrows of any tournament (complete directed graph) on $n$ vertices.
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Cited by 1 Pith paper
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Complexity of Unambiguous Problems in $\Sigma^P_2$
Unambiguous Σ^P_2 problems are captured by three syntactic classes (PTW, PCW, PMA) that all lie in S^P_2, with several concrete problems proven complete for these classes.
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