{"id":"W1980126517","doi":"10.1142/s0218216501001104","title":"COMPUTING THE JONES POLYNOMIAL ON BIPARTITE GRAPHS","year":2001,"lang":"en","type":"article","venue":"Journal of Knot Theory and Its Ramifications","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Bipartite graph; Bracket polynomial; Combinatorics; Knot polynomial; Jones polynomial; HOMFLY polynomial; Knot (papermaking); Alexander polynomial; Knot invariant; Discrete mathematics; Quantum invariant; Complete bipartite graph; Knot theory; Crossing number (knot theory); Graph; Polynomial; Matrix polynomial; Square-free polynomial","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":[0.0013166,0.00008142304,0.0001629404,0.0001946242,0.0002923711,0.00002919056,0.0001814519,0.00004669704,0.00009923179],"category_scores_gemma":[0.001113098,0.00004848896,0.0000836086,0.0003308829,0.0001027269,0.00007005119,0.00002163374,0.0002254699,0.0000164898],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009033632,"about_ca_system_score_gemma":0.00002794935,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":4.95519e-7,"about_ca_topic_score_gemma":7.899105e-7,"domain_scores_codex":[0.9990792,0.0002427962,0.00035117,0.00007589275,0.0001167428,0.0001341585],"domain_scores_gemma":[0.9973592,0.002019439,0.0003132039,0.0001405135,0.000104376,0.00006322256],"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":[0.0000647237,0.0001190949,0.0001895474,0.000005638658,0.00005121565,0.000003888014,0.0007211934,0.00001559782,0.0003378181,0.9888639,0.001786651,0.007840667],"study_design_scores_gemma":[0.0008412949,0.0003346208,0.01767815,0.00006996337,0.0001702222,0.0006885723,0.002331358,0.0002304912,0.0004826683,0.9481096,0.02887964,0.0001833931],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9893103,0.0008204584,0.003848297,0.00374493,0.0002797381,0.00008494779,0.00000236881,0.0000133937,0.001895585],"genre_scores_gemma":[0.9981288,0.0002255749,0.0002251392,0.0002515281,0.0002295749,8.900873e-7,3.606996e-7,0.000007457465,0.0009307183],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04075433,"threshold_uncertainty_score":0.2248711,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04476554547116283,"score_gpt":0.3198933932761936,"score_spread":0.2751278478050307,"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."}}