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- W2912348161 abstract "A generalized $N$-sided die is a random variable $D$ on a sample space of $N$ equally likely outcomes taking values in the set of positive integers. We say of independent $N$ sided dice $D_i, D_j$ that $D_i$ beats $D_j$, written $D_i to D_j$, if $Prob(D_i > D_j) > frac{1}{2} $. Examples are known of intransitive $6$-sided dice, i.e. $D_1 to D_2 to D_3$ but $D_3 to D_1$. A tournament of size $n$ is a choice of direction $i to j$ for each edge of the complete graph on $n$ vertices. We show that if $R$ is tournament on the set ${ 1, dots, n }$, then for sufficiently large $N$ there exist sets of independent $N$-sided dice ${ D_1, dots, D_n }$ such that $D_i to D_j$ if and only if $i to j$ in $R$." @default.
- W2912348161 created "2019-02-21" @default.
- W2912348161 creator A5006701906 @default.
- W2912348161 date "2019-01-28" @default.
- W2912348161 modified "2023-09-27" @default.
- W2912348161 title "Generalized Intransitive Dice: Mimicking an Arbitrary Tournament" @default.
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