{"paper":{"title":"Betweenness and Nonbetweenness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ross Atkins","submitted_at":"2016-02-18T13:44:53Z","abstract_excerpt":"The betweenness function $bet(n)$ is the minimum number of total orderings of $n$ objects such that for any three distinct objects $a$, $b$ and $c$, there is an ordering in which $b$ is between $a$ and $c$. The nonbetweenness function $nbet(n)$ is the minimum number of total orderings such that for any three distinct objects $a$, $b$ and $c$, there is an ordering in which $b$ is not between $a$ and $c$. We show that $nbet(n) = \\left\\lceil \\log_2\\log_2n \\right\\rceil+1$ and $bet(n) = \\Theta(\\log n)$. Betweenness and Nonbetweenness are specific cases of a more general extreme value function calle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05798","kind":"arxiv","version":1},"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"}