{"id":"W2053952882","doi":"10.1016/j.disc.2008.05.003","title":"Independence polynomials of circulants with an application to music","year":2008,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":30,"is_retracted":false,"has_abstract":false,"ca_institutions":"Dalhousie University","funders":"","keywords":"Mathematics; Combinatorics; Discrete mathematics; Cardinality (data modeling); Complement (music); Independence (probability theory); Graph; Polynomial; Tutte polynomial; Voltage 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":[0.0004231068,0.0003416715,0.0007199789,0.0001622604,0.0001394642,0.00001945619,0.0006166605,0.0001444362,0.00003968582],"category_scores_gemma":[0.0005392406,0.0002797589,0.00008499569,0.0004906702,0.0001472946,0.0002650626,0.0001285785,0.0001852527,0.00005279122],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007322885,"about_ca_system_score_gemma":0.0001009465,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000012491,"about_ca_topic_score_gemma":0.00001780201,"domain_scores_codex":[0.9975023,0.00005392276,0.0007983284,0.0003950085,0.0008650346,0.0003853719],"domain_scores_gemma":[0.9971497,0.0004045679,0.0005788257,0.001339731,0.0002895109,0.0002376547],"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":[0.0001566717,0.001673377,0.0006955265,0.001578904,0.0001736344,0.00004721206,0.02435282,0.0003040814,0.02148197,0.948078,0.0004032278,0.001054617],"study_design_scores_gemma":[0.001082676,0.0006665333,0.0002617255,0.0003730327,0.0001362776,0.000252771,0.001828887,0.00299564,0.02751187,0.9640253,0.00008724777,0.0007780409],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6380374,0.000009382054,0.3587302,0.00003155437,0.00006608659,0.000953073,0.00002042135,0.0001537275,0.001998203],"genre_scores_gemma":[0.7468604,0.000003442763,0.2527191,0.00003297733,0.00006559172,0.0001060133,0.000006270627,0.00008161309,0.0001246067],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.108823,"threshold_uncertainty_score":0.9999654,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04803095456035274,"score_gpt":0.3116860197054583,"score_spread":0.2636550651451056,"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."}}