{"id":"W2950000083","doi":"10.48550/arxiv.1108.4045","title":"Character-theoretic Techniques for Near-central Enumerative Problems","year":2011,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Centralizer and normalizer; Combinatorics; Factorization; Mathematics; Enumeration; Genus; Cluster algebra; Character (mathematics); Algebra over a field; Pure mathematics; Physics; Geometry; Algorithm","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003911592,0.001432515,0.001354157,0.005345527,0.004326512,0.005258682,0.003811703,0.002676717,0.01378392],"category_scores_gemma":[0.01852212,0.0009209175,0.002193117,0.003832872,0.006634743,0.01430455,0.009497993,0.008166632,0.002494974],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002610922,"about_ca_system_score_gemma":0.001120669,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005563277,"about_ca_topic_score_gemma":0.0008483842,"domain_scores_codex":[0.9961715,0.001370058,0.0002826139,0.0008157643,0.0008711574,0.0004887938],"domain_scores_gemma":[0.9885429,0.00640631,0.0007691033,0.00245828,0.001254866,0.0005685782],"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":[0.00001459581,0.00002991794,0.0002386075,0.00004102641,0.000004559272,0.00003817719,0.0003287556,0.0007827358,0.000384238,0.9887069,0.001109169,0.008321229],"study_design_scores_gemma":[0.00000846526,0.0000117049,0.00007286234,0.0000185625,0.000007011445,0.00006079957,0.0001160521,0.009819987,0.0006258221,0.985526,0.003719859,0.00001281772],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08888955,0.0006480276,0.8236831,0.002900226,0.0004097964,0.0001967808,0.0003219137,0.0008248696,0.0821258],"genre_scores_gemma":[0.5629447,0.0008965659,0.3889461,0.00123376,0.001404617,0.0008487787,0.001056104,0.0007719662,0.04189744],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01378392,"threshold_uncertainty_score":0.04611182,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09911985963071701,"score_gpt":0.2173769046241164,"score_spread":0.1182570449933993,"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."}}