{"paper":{"title":"Toward Lower Bounds for Chromatic Symmetric Functions in the Elementary Basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Isaiah Siegl","submitted_at":"2025-09-02T21:20:53Z","abstract_excerpt":"Tatsuyuki Hikita recently proved the Stanley--Stembridge conjecture using probabilistic methods, showing that the chromatic symmetric functions of unit interval graphs are $e$-positive. Finding a combinatorial interpretation for these $e$-coefficients remains a major open problem. One approach is to look for combinatorial interpretations which are subsets of Gasharov's $P$-tableaux. Towards this goal, we introduce sets of strong and powerful $P$-tableaux, and use them to find combinatorial interpretations for various $e$-coefficients of the chromatic symmetric function $X_{inc(P)}(\\mathbf{x}, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.02841","kind":"arxiv","version":3},"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/2509.02841/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"}