{"paper":{"title":"P\\'olya theory for species with an equivariant group action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Gainer-Dewar","submitted_at":"2014-01-23T22:03:34Z","abstract_excerpt":"Joyal's theory of combiantorial species provides a rich and elegant framework for enumerating combinatorial structures by translating structural information into algebraic functional equations. We present some classical and folklore results which interpret the species-theoretic cycle index series in terms of the P\\'{o}lya theory of the action of the symmetric group on the label set, allowing the enumeration of \"partially-labeled\" structures and providing an alternate foundation for several proofs. We also extend the theory to incorporate information about \"structural\" group actions (i.e. those"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6202","kind":"arxiv","version":4},"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"}