{"paper":{"title":"Unit Interval Orders of Open and Closed Intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan Shuchat, Ann Trenk, Randy Shull","submitted_at":"2015-01-26T15:04:39Z","abstract_excerpt":"A poset $P = (X,\\prec)$ is a unit OC interval order if there exists a representation that assigns an open or closed real interval $I(x)$ of unit length to each $x \\in P$ so that $x \\prec y$ in $P$ precisely when each point of $I(x)$ is less than each point in $I(y)$. In this paper we give a forbidden poset characterization of the class of unit OC interval orders and an efficient algorithm for recognizing the class. The algorithm takes a poset $P $ as input and either produces a representation or returns a forbidden poset induced in $P$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06430","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"}