{"paper":{"title":"A deletion-contraction formula and monotonicity properties for the polymatroid Tutte polynomial","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tam\\'as K\\'alm\\'an, Xian'an Jin, Xiaxia Guan","submitted_at":"2023-09-24T13:43:24Z","abstract_excerpt":"The Tutte polynomial is a fundamental invariant of matroids. The polymatroid Tutte polynomial $\\mathscr{T}_{P}(x,y)$, introduced by Bernardi, K\\'{a}lm\\'{a}n, and Postnikov, is an extension of the classical Tutte polynomial from matroids to polymatroids $P$. In this paper, we first obtain a deletion-contraction formula for $\\mathscr{T}_{P}(x,y)$. Then we prove two natural properties of coefficientwise monotonicity, one for containment and one for minors, both for the interior polynomial $x^{n}\\mathscr{T}_{P}(x^{-1},1)$ and the exterior polynomial $y^{n}\\mathscr{T}_{P}(1,y^{-1})$, where $P$ is a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.13639","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/2309.13639/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"}