{"paper":{"title":"On bar lengths in partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Jean-Baptiste Gramain, Jorn B. Olsson","submitted_at":"2011-01-26T14:47:11Z","abstract_excerpt":"In this paper, we present, given a odd integer $d$, a decomposition of the multiset of bar lengths of a bar partition $\\lambda$ as the union of two multisets, one consisting of the bar lengths in its $\\bar{d}$-core partition $\\bar{c}_d(\\lambda)$ and the other consisting of modified bar lengths in its $\\bar{d}$-quotient partition. In particular, we obtain that the multiset of bar lengths in $\\bar{c}_d(\\lambda)$ is a sub-multiset of the multiset of bar lengths in $\\lambda$. Also we obtain a relative bar formula for the degrees of spin characters of the Schur extensions of the symmetric group. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5071","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":""},"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"}