{"paper":{"title":"Towards a q-analogue of the Harer-Zagier formula via rook placements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Max Wimberley","submitted_at":"2014-12-10T02:39:42Z","abstract_excerpt":"In 1986 Harer and Zagier computed a certain matrix integral to determine an influential closed-form formula for the number of (orientable) one-face maps on n vertices colored from N colors. Kerov (1997) provided a proof which computed the same matrix integral differently, which gave an interpretation of these numbers as also counting the number of placements of non-attacking rooks on Young diagrams. Bernardi (2010) provided a bijective proof of this formula by putting one-face maps in bijection with tree-rooted maps, which are orientable maps with a designated spanning tree. In the first part "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3182","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":""},"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"}