{"paper":{"title":"Stable curves and chromatic polynomials","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Bernhard Reinke, Rob Silversmith","submitted_at":"2024-11-26T16:14:51Z","abstract_excerpt":"The intersection numbers of moduli spaces of stable curves $\\overline{M}_{g,m}$ are well-studied and are known to have rich combinatorial structure. We introduce a natural class of these intersection numbers $\\omega_{G,g,m}$ indexed by finite simple graphs $G=(V,E)$. In genus zero, these numbers are closely related to several previously-studied quantities, including maximum likelihood degrees in algebraic statistics, counts of regions of certain hyperplane arrangements, and Kapranov degrees. We give two proofs of a simple closed formula $\\omega_{G,g,m}=(-1)^{\\left\\lvert V \\right\\rvert}\\chi_G(-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17551","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.17551/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}