{"paper":{"title":"Character factorisations, $z$-asymmetric partitions and plethysm","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Seamus Albion","submitted_at":"2025-01-30T17:34:26Z","abstract_excerpt":"The Verschiebung operators $\\varphi_t $ are a family of endomorphisms on the ring of symmetric functions, one for each integer $t\\geq2$. Their action on the Schur basis has its origins in work of Littlewood and Richardson, and is intimately related with the decomposition of a partition into its $t$-core and $t$-quotient. Namely, they showed that the action on $s_\\lambda$ is zero if the $t$-core of the indexing partition is nonempty, and otherwise it factors as a product of Schur functions indexed by the $t$-quotient. Much more recently, Lecouvey and, independently, Ayyer and Kumari have provid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18520","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.18520/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"}