{"paper":{"title":"Generalized Intransitive Dice: Mimicking an Arbitrary Tournament","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ethan Akin","submitted_at":"2019-01-28T01:10:41Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09477","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}