{"paper":{"title":"On a conjecture of Las Vergnas","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gordon F. Royle, Steven D. Noble","submitted_at":"2026-06-10T17:06:08Z","abstract_excerpt":"In 1988, Las Vergnas conjectured that if $M$ is a binary matroid with bicycle dimension $d$, then for $0 \\leq k \\leq d$, the $k$th derivative of the diagonal Tutte polynomial $T(M;z,z)$ evaluated at $z=-1$ is an integer multiple of $2^{d-k}$. While this was rapidly disproved for binary matroids and for graphs in general, extensive computations strongly suggested that it might be true for planar graphs. In this paper we prove that this is indeed the case. To do this, we consider a stronger divisibility property that we call the LV property, and a larger class of graphs, namely the class of delt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12335","kind":"arxiv","version":1},"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/2606.12335/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"}