{"id":"W3045345952","doi":"","title":"A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function","year":2020,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Chromatic polynomial; Combinatorics; Tutte polynomial; Mathematics; Chromatic scale; Symmetric function; Vertex (graph theory); Spanning tree; Discrete mathematics; Graph; Line graph","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003263121,0.0007422807,0.001062722,0.001172233,0.0003069693,0.0001306971,0.0005049614,0.0004829683,0.00004725298],"category_scores_gemma":[0.0008028344,0.0007616795,0.0002211729,0.003660536,0.0002694018,0.0003690401,0.0008166436,0.001126628,0.00004451519],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003484027,"about_ca_system_score_gemma":0.0002171314,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002442205,"about_ca_topic_score_gemma":0.000007668366,"domain_scores_codex":[0.9970275,0.0002231227,0.0005961275,0.001294726,0.0003191509,0.0005394135],"domain_scores_gemma":[0.9959079,0.001372433,0.001022352,0.0009647047,0.0003934134,0.0003392025],"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":[0.0002120858,0.0002099998,0.002570009,0.001595665,0.0005774317,0.0001379831,0.0001550083,0.000334519,0.00003731475,0.9936538,0.0001018423,0.0004143268],"study_design_scores_gemma":[0.002158591,0.0004802263,0.0003907701,0.000486103,0.001694611,0.00004450664,0.0006431375,0.02539183,0.00004862299,0.9678184,0.00003589782,0.0008072654],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6423268,0.0001419313,0.3520547,0.00003107356,0.001099192,0.000998111,0.000020654,0.00061647,0.002711054],"genre_scores_gemma":[0.9928448,0.00008158322,0.006600726,0.00004882265,0.0001045831,0.000006678482,0.00002522432,0.0001182043,0.0001694177],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.350518,"threshold_uncertainty_score":0.9994834,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07808410023771048,"score_gpt":0.2045727153342852,"score_spread":0.1264886150965747,"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."}}