{"paper":{"title":"Reciprocal maximum likelihood degrees of diagonal linear concentration models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.CO","stat.TH"],"primary_cat":"math.ST","authors_text":"Christopher Eur, Jos\\'e Alejandro Samper, Tara Fife, Tim Seynnaeve","submitted_at":"2020-11-28T18:13:50Z","abstract_excerpt":"We show that the reciprocal maximal likelihood degree (rmld) of a diagonal linear concentration model $\\mathcal L \\subseteq \\mathbb{C}^n$ of dimension $r$ is equal to $(-2)^r\\chi_M( \\textstyle\\frac{1}{2})$, where $\\chi_M$ is the characteristic polynomial of the matroid $M$ associated to $\\mathcal L$. In particular, this establishes the polynomiality of the rmld for general diagonal linear concentration models, positively answering a question of Sturmfels, Timme, and Zwiernik."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.14182","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/2011.14182/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"}