{"paper":{"title":"A Nekrasov-Okounkov Type formula for $\\widetilde{C}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Mathias P\\'etr\\'eolle","submitted_at":"2015-05-06T09:42:35Z","abstract_excerpt":"In 2008, Han rediscovered an expansion of powers of Dedekind $\\eta$ function attributed to Nekrasov and Okounkov (which was actually first proved the same year by Westbury) by using a famous identity of Macdonald in the framework of type $\\widetilde{A}$ affine root systems. In this paper, we obtain new combinatorial expansions of powers of $\\eta$, in terms of partition hook lengths, by using the Macdonald identity in type $\\widetilde{C}$ and a new bijection between vectors with integral coordinates and a subset of $t$-cores for integer partitions. As applications, we derive a symplectic hook f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01295","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"}