{"id":"W4388938474","doi":"10.1002/jgt.23060","title":"A graph polynomial from chromatic symmetric functions","year":2023,"lang":"en","type":"article","venue":"Journal of Graph Theory","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Chromatic polynomial; Mathematics; Tutte polynomial; Combinatorics; Chromatic scale; Symmetric function; Discrete mathematics; Elementary symmetric polynomial; Graph; Symmetric polynomial; Polynomial; Matrix polynomial; Voltage graph; Line graph; Orthogonal polynomials; Mathematical analysis; Difference polynomials","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001300571,0.0002318131,0.000596121,0.001303895,0.0001659424,0.00004926844,0.0004666433,0.0001271165,0.0001549251],"category_scores_gemma":[0.002835991,0.0001891539,0.0004869947,0.002165547,0.0001146463,0.000267939,0.00008776122,0.0004392507,0.0001411699],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007633254,"about_ca_system_score_gemma":0.00008155984,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002445351,"about_ca_topic_score_gemma":0.000001526779,"domain_scores_codex":[0.997719,0.0002598107,0.0009482845,0.0001568985,0.0005872562,0.0003287128],"domain_scores_gemma":[0.9944173,0.003827656,0.0009149355,0.0004506857,0.0002148989,0.0001745365],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0003358173,0.0006578062,0.0002488681,0.0002120411,0.001049227,0.0002754321,0.001980745,0.00005381375,0.004212304,0.9423951,0.04384691,0.004731949],"study_design_scores_gemma":[0.001045,0.000200514,0.0003350561,0.0001708895,0.0002705182,0.00008981561,0.0009641874,0.0000434366,0.0004802878,0.9957433,0.0004678108,0.0001891892],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9534953,0.0005132621,0.0380713,0.0002611572,0.004384275,0.0002790967,0.00003167016,0.0002584544,0.002705464],"genre_scores_gemma":[0.9867956,0.0001149243,0.01137527,0.00005167332,0.0008560941,0.00001236013,0.00000365536,0.00009109275,0.0006993134],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05334821,"threshold_uncertainty_score":0.7713474,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03316427340480621,"score_gpt":0.2986389176558069,"score_spread":0.2654746442510006,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}