{"paper":{"title":"Poset probability in two-row partition posets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Albin Jaldevik, Jan Snellman","submitted_at":"2025-01-19T15:21:09Z","abstract_excerpt":"We find explicit formulae for poset probabilities \\(\\mathbf{Prob}(P_\\lambda; \\alpha < \\beta)\\) in partition posets (cell posets) \\(P_{\\lambda}\\) when \\(\\lambda=(\\lambda_{1},\\lambda_{2})\\) is a two-row partition. These probabilities are given as rational expressions in \\(f^{\\sigma / \\tau}\\), where \\(\\tau \\subseteq \\sigma \\subseteq \\lambda\\). We then use well-known formulae, such as the hook-length formula for \\(f^\\lambda\\), the number of standard Young tableaux on a partition \\(\\lambda\\), and the corresponding determinantal formula by Jacobi-Trudi-Aitken for \\(f^{\\lambda / \\mu}\\), the number of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.11073","kind":"arxiv","version":5},"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/2501.11073/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"}