{"paper":{"title":"Infinite sequences via Lie algebra actions for oligomorphic groups","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CO","math.GR","math.LO"],"primary_cat":"math.RT","authors_text":"Zbigniew Wojciechowski","submitted_at":"2026-03-25T00:38:58Z","abstract_excerpt":"Many integer sequences arise as numbers of $G$-orbits on $\\binom{X}{n}$ as $n$ varies, for a permutation group $G\\subseteq \\operatorname{Sym}(X)$. For finite $X$, Stanley proved that these finite sequences increase towards the middle using an action of the Lie algebra $\\mathfrak{sl}_2(\\mathbb{C})$. For infinite sets $X$, and hence infinite sequences, Cameron provided an argument for monotonicity by identifying orbits with a vector space basis of the orbit algebra $\\mathsf{H}_{G,X}^{\\star}$, and proving injectivity of a certain operator $\\mathsf{H}_{G,X}^{\\star}\\to \\mathsf{H}_{G,X}^{\\star+1}$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.23809","kind":"arxiv","version":2},"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/2603.23809/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"}