{"paper":{"title":"On the Basis of the Burnside Ring of a Fusion System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.AT","authors_text":"Ergun Yalcin, Matthew Gelvin, Sune Precht Reeh","submitted_at":"2014-03-24T17:39:21Z","abstract_excerpt":"We consider the Burnside ring $A(\\mathcal{F})$ of $\\mathcal{F}$-stable $S$-sets for a saturated fusion system $\\mathcal{F}$ defined on a $p$-group $S$. It is shown by S. P. Reeh that the monoid of $\\mathcal{F}$-stable sets is a free commutative monoid with canonical basis $\\{\\alpha_P\\}$. We give an explicit formula that describes $\\alpha_P$ as an $S$-set. In the formula we use a combinatorial concept called broken chains which we introduce to understand inverses of modified M\\\"obius functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6053","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"}