{"paper":{"title":"Coefficients of univariate Tutte polynomials with one variable fixed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tianlong Ma, Xian'an Jin, Xiaxia Guan","submitted_at":"2025-03-08T06:58:05Z","abstract_excerpt":"It is well known that the 2-variable Tutte polynomials contain chromatic polynomial and flow polynomial of graphs, i.e. the cases of $y=0$ and $x=0$. In 2013, K\\'{a}lm\\'{a}n introduced the interior and exterior polynomials which generalized the cases of $y=1$ and $x=1$ of Tutte polynomials of graphs to hypergraphs, and further polymatroids. There have been some results on coefficients of these polynomials, which motivate us to study uniformly the coefficients of $T_M(x,t)$ and $T_M(t,y)$, where $M$ is a matroid and $t$ is a fixed real number. In this paper, we introduce two mutually dual param"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.06095","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/2503.06095/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"}