{"paper":{"title":"An infinite family of counterexamples to the Stanley--Gasharov conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David G. L. Wang, K. Zhang, T.Y. Zhao","submitted_at":"2026-07-29T17:41:57Z","abstract_excerpt":"The Stanley--Gasharov conjecture asserts that the chromatic symmetric function of every claw-free graph is Schur-positive. Prajapati, and independently Matherne and Morales, found counterexamples, and the latter asked for an infinite family of counterexamples. Combining Prajapati's complete census through order~$12$ with an exact census of the $144{,}492$ previously untreated connected claw-free graphs on~$n$ vertices and~$m$ edges with $13\\le n\\le 21$ and $n-1\\le m\\le 20$, we show that their counterexample graph~$G_2$ with $12$ vertices and $21$ edges is the unique minimum counterexample unde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27166","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/2607.27166/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"}