{"paper":{"title":"Factorization of Schur polynomials twisted by roots of unity and a reciprocal pair","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Carles Mar\\'in","submitted_at":"2026-08-10T13:58:23Z","abstract_excerpt":"Let $\\mu_t$ be the full set of $t$-th roots of unity and $(z,z^{-1})$ a free reciprocal pair. We determine how much of a partition $s_\\lambda(\\mu_t,z,z^{-1})$ can see: a multiset of three integers and a sign, and nothing else, so partitions of any sizes agreeing on it share the value. The evaluation, for every $t\\ge2$ and every $\\lambda$ with no hypothesis on its shape, is a signed product of exactly three factors over a fixed denominator, or zero, the three arguments read off the $t$-quotient. The proof is a Laplace expansion along the $t$ frozen rows of the bialternant with one cancellation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09619","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/2608.09619/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"}