{"paper":{"title":"Ordered set partition posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.RT"],"primary_cat":"math.CO","authors_text":"Bruce E Sagan (Michigan State University), Sheila Sundaram (University of Minnesota)","submitted_at":"2025-06-29T18:20:31Z","abstract_excerpt":"A set partition is said to be ordered if the blocks of the partition are listed in a specific order. The ordered set partitions of $\\{1,\\ldots,n\\}$, with a unique minimal element adjoined, form a lattice $\\Om_n$ with respect to refinement. The lattice $\\Om_n$ is well known to be the face lattice of the permutohedron. In this paper we study the combinatorics and topology of two subposets of $\\Om_n$ with restricted block sizes, either all divisible by some fixed $d\\ge2$, or all congruent to $1$ modulo $d$. For the $d$-divisible case we derive an explicit recursive atom ordering for the lattice, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23355","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.23355/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}