{"id":"W2015046561","doi":"10.1007/s00026-006-0300-z","title":"A Symmetric Function Resolution of the Number of Permutations With Respect to Block-Stable Elements","year":2006,"lang":"en","type":"article","venue":"Annals of Combinatorics","topic":"semigroups and automata theory","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Combinatorics; Partition (number theory); Block (permutation group theory); Resolution (logic); Discrete mathematics","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":[0.002033256,0.000930402,0.001459592,0.002469602,0.001899566,0.004089258,0.002221033,0.001445649,0.01165587],"category_scores_gemma":[0.00582044,0.0006847555,0.001605149,0.002014167,0.003044057,0.009055778,0.002844319,0.003732739,0.002327505],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001323794,"about_ca_system_score_gemma":0.0009532143,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004171205,"about_ca_topic_score_gemma":0.0003804189,"domain_scores_codex":[0.998017,0.0005745951,0.0001364458,0.0004816165,0.0004481532,0.0003422179],"domain_scores_gemma":[0.9958689,0.002152322,0.0003072879,0.0006410656,0.0004669161,0.0005635199],"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":[0.00009819926,0.00003105993,0.0001299316,0.00003779563,0.00001399264,0.00006901858,0.0001526805,0.001213166,0.00303336,0.9818168,0.001137292,0.0122668],"study_design_scores_gemma":[0.00002382205,0.00004424797,0.0001824544,0.00001556573,0.0000281043,0.0002118499,0.00008552772,0.01095379,0.005292586,0.9786212,0.004509705,0.00003116472],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1984426,0.001014915,0.7221344,0.001422284,0.0005421249,0.0001060741,0.0004885259,0.000843498,0.07500549],"genre_scores_gemma":[0.8195525,0.000607147,0.1429668,0.0004640685,0.0007879814,0.0001701803,0.0005654145,0.0004949354,0.03439102],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01165587,"threshold_uncertainty_score":0.03899276,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01986403438404554,"score_gpt":0.2686542668971128,"score_spread":0.2487902325130673,"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."}}