{"paper":{"title":"Interval Orders with Two Interval Lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ann N Trenk, Garth Isaak, Simona Boyadzhiyska","submitted_at":"2017-07-25T17:15:25Z","abstract_excerpt":"A poset $P = (X,\\prec)$ has an interval representation if each $x \\in X$ can be assigned a real interval $I_x$ so that $x \\prec y$ in $P$ if and only if $I_x$ lies completely to the left of $I_y$. Such orders are called \\emph{interval orders}. In this paper we give a surprisingly simple forbidden poset characterization of those posets that have an interval representation in which each interval length is either 0 or 1. In addition, for posets $(X,\\prec)$ with a weight of 1 or 2 assigned to each point, we characterize those that have an interval representation in which for each $x \\in X$ the len"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08093","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"}