{"id":"W2404238687","doi":"","title":"A Property of the Roots of r-D Rook Polynomials.","year":2010,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Property (philosophy); Combinatorics; Pure mathematics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000206346,0.00008553443,0.0001532625,0.00004131187,0.00005885312,0.00002147821,0.0009817333,0.00005139205,0.000008890564],"category_scores_gemma":[0.00008048784,0.00004838944,0.00008519289,0.0003062877,0.00009024329,0.0001722103,0.0003270945,0.0001467751,0.000007689163],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009523133,"about_ca_system_score_gemma":0.0001402991,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000115809,"about_ca_topic_score_gemma":0.00001818562,"domain_scores_codex":[0.999187,0.00004694596,0.0002449302,0.0001680352,0.0002137184,0.0001393541],"domain_scores_gemma":[0.9990795,0.0000564717,0.0001801679,0.0005457839,0.0000933,0.0000447461],"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":[0.000005815628,0.0001211025,0.002039848,0.00001479307,0.00001186556,5.885496e-7,0.0002405102,0.000006899267,0.1569672,0.8239262,0.0007793571,0.01588576],"study_design_scores_gemma":[0.0009695324,0.0001396171,0.09523421,0.0000513471,0.00001024843,0.000008463539,0.000007414528,0.005801232,0.3178147,0.5772092,0.002543721,0.0002103075],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9939067,0.00002004276,0.0002828049,0.0007292567,0.002554254,0.0001523529,0.000001079617,0.00003405051,0.00231949],"genre_scores_gemma":[0.9987836,4.532073e-7,0.0008062836,0.00004675274,0.00001004804,0.000004598074,2.649238e-7,0.000004861531,0.0003431763],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2467171,"threshold_uncertainty_score":0.1973264,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008091183198022657,"score_gpt":0.2146662831715901,"score_spread":0.2065750999735675,"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."}}