{"id":"W4415667466","doi":"10.55016/ojs/cdm.v20i2.76682","title":"A generalization of the Beraha–Kahane–Weiss theorem with graph polynomial applications","year":2025,"lang":"","type":"article","venue":"Contributions to Discrete Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Chromatic polynomial; Tutte polynomial; Factor theorem; Graph property; Graph; Voltage graph; Polynomial; Generalization; Cubic graph","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001392112,0.0009531039,0.0007829134,0.002452471,0.001274629,0.001228557,0.001245368,0.001025933,0.004978348],"category_scores_gemma":[0.008906891,0.000375852,0.001164549,0.002080533,0.00279969,0.004525754,0.001956768,0.003021522,0.001306004],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009443711,"about_ca_system_score_gemma":0.0006393727,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001565229,"about_ca_topic_score_gemma":0.0009550707,"domain_scores_codex":[0.9993393,0.000181379,0.00002689854,0.0001688489,0.0001707273,0.0001128618],"domain_scores_gemma":[0.9979079,0.001079609,0.0002034877,0.0002729397,0.0003534936,0.0001824769],"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":[0.00001515619,0.0000141409,0.0002106171,0.00004650873,0.000006231494,0.00007037594,0.0001232575,0.003826706,0.001073387,0.9807011,0.002015258,0.01189727],"study_design_scores_gemma":[0.000008564178,0.00002181636,0.0002606525,0.00002107964,0.000008005525,0.000194228,0.00004321967,0.03643201,0.0009877319,0.9508334,0.01116933,0.00001992441],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06107217,0.002067205,0.87085,0.002661292,0.0005977109,0.00005689151,0.0002349987,0.0002887996,0.06217085],"genre_scores_gemma":[0.8161189,0.004664291,0.1282637,0.00145424,0.001965724,0.0001836915,0.0002674937,0.0004393049,0.04664262],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004978348,"threshold_uncertainty_score":0.01665425,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007507840799624974,"score_gpt":0.2952647826141136,"score_spread":0.2877569418144886,"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."}}