{"id":"W4381826794","doi":"10.48550/arxiv.2306.12506","title":"Promotion permutations for tableaux","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Österreichischen Akademie der Wissenschaften; Austrian Science Fund; Simons Foundation Autism Research Initiative; Natural Sciences and Engineering Research Council of Canada; Johns Hopkins University; North Dakota State University; National Science Foundation","keywords":"Bijection; Young tableau; Combinatorics; Basis (linear algebra); Promotion (chess); Representation (politics); Algebraic number; Computer science; Action (physics); Rotation (mathematics); Mathematics; Algebra over a field; Pure mathematics; Artificial intelligence; Physics; Geometry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002012637,0.0002454978,0.0002967458,0.0001996745,0.0001861141,0.00003514703,0.0004519822,0.0002985351,0.00006048199],"category_scores_gemma":[0.0005362463,0.0003043074,0.0002146127,0.0002849069,0.00007667382,0.0001298527,0.000482866,0.0003988573,0.0001007464],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002683068,"about_ca_system_score_gemma":0.0001282363,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001254863,"about_ca_topic_score_gemma":0.00006993239,"domain_scores_codex":[0.9986795,0.00005034019,0.0002115859,0.0006954691,0.00006823753,0.0002948592],"domain_scores_gemma":[0.9982446,0.0004563525,0.0002571602,0.0007278626,0.0002305352,0.0000834452],"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":[0.00001348263,0.00009136891,0.0001589351,0.0003980791,0.00008754544,0.00003308774,0.0001542731,0.01174421,0.00001767904,0.9859745,0.001229829,0.00009704384],"study_design_scores_gemma":[0.0003521472,0.00004682292,0.00007706702,0.0001086078,0.0001700078,0.000001333148,0.0001497801,0.02611684,0.0001068476,0.9720813,0.0004960138,0.0002932226],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1801328,0.000008411891,0.8156551,0.000168504,0.0007690486,0.001067606,0.0001435807,0.0005783098,0.001476715],"genre_scores_gemma":[0.94893,0.00004849246,0.01844963,0.00001681474,0.000214564,0.00001848934,0.0001444974,0.00009327912,0.03208421],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7972054,"threshold_uncertainty_score":0.9999409,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.317995583819259,"score_gpt":0.2860231305704671,"score_spread":0.03197245324879189,"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."}}