{"id":"W1486890707","doi":"10.37236/199","title":"Composition of Transpositions and Equality of Ribbon Schur $Q$-Functions","year":2009,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Skew; Schur's lemma; Combinatorics; Schur's theorem; Ribbon; Diagram; Eulerian path; Schur algebra; Substitution (logic); Irreducibility; Pure mathematics; Discrete mathematics; Orthogonal polynomials; Geometry; Lagrangian; Gegenbauer polynomials; Computer science","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":[0.001145245,0.000153377,0.000504109,0.0001239068,0.0001161965,0.00001000368,0.0002948141,0.0000821509,0.000005817411],"category_scores_gemma":[0.0002240824,0.0001159226,0.0001640405,0.0003949855,0.0001186896,0.000175525,0.00001808547,0.0005158141,4.621085e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001534976,"about_ca_system_score_gemma":0.0001746997,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002061159,"about_ca_topic_score_gemma":0.000001139717,"domain_scores_codex":[0.9981067,0.0001834094,0.0008910465,0.00008494842,0.0004528868,0.000281065],"domain_scores_gemma":[0.9972862,0.0008010406,0.001043294,0.0003015002,0.0005074688,0.00006047698],"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":[0.00009720321,0.0006139188,0.00002211616,0.00007363259,0.00008489715,8.267506e-7,0.0005329823,0.00003071398,0.008545097,0.9896487,0.00005782175,0.0002921156],"study_design_scores_gemma":[0.00111831,0.001347981,0.0001741595,0.0001246579,0.0002773389,0.000100686,0.0001914062,0.00006394354,0.01453015,0.9818961,0.00007719365,0.00009809325],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8358021,0.001156927,0.1611153,0.0006972828,0.0002625868,0.0002361274,0.000006923306,0.00001949722,0.0007032752],"genre_scores_gemma":[0.9990538,0.0002790566,0.0005588752,0.00001440879,0.00004124277,0.000001401866,0.00000106706,0.00001409127,0.00003610945],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1632517,"threshold_uncertainty_score":0.4727188,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02045735255392491,"score_gpt":0.3009647153715366,"score_spread":0.2805073628176117,"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."}}