{"paper":{"title":"A direct proof of well-definedness for the polymatroid Tutte polynomial","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xian'an Jin, Xiaxia Guan","submitted_at":"2024-03-09T07:25:51Z","abstract_excerpt":"For a polymatroid $P$ over $[n]$, Bernardi, K\\'{a}lm\\'{a}n and Postnikov [\\emph{Adv. Math.} 402 (2022) 108355] introduced the polymatroid Tutte polynomial $\\mathscr{T}_{P}$ relying on the order $1<2<\\cdots<n$ of $[n]$, which generalizes the classical Tutte polynomial from matroids to polymatroids. They proved the independence of this order by the fact that $\\mathscr{T}_{P}$ is equivalent to another polynomial that only depends on $P$. In this paper, similar to the Tutte's original proof of the well-definedness of the Tutte polynomial defined by the summation over all spanning trees using activ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.05825","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/2403.05825/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"}