{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005066692,0.0003117601,0.000267897,0.000554165,0.001128912,0.00195172,0.0005168208,0.0005187085,0.01099122],"category_scores_gemma":[0.001458558,0.0002653226,0.0004714882,0.0006174098,0.001666197,0.002453195,0.001084366,0.001502574,0.002396372],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007487633,"about_ca_system_score_gemma":0.0004990301,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005401668,"about_ca_topic_score_gemma":0.001013718,"domain_scores_codex":[0.9994953,0.0001177781,0.00003464918,0.0001000478,0.0001732958,0.0000790086],"domain_scores_gemma":[0.9995379,0.000154705,0.00004412613,0.0001158267,0.00008403252,0.00006346975],"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":[0.000005031516,0.000004276672,0.00003785301,0.00001122748,7.547681e-7,0.00002279032,0.00006497182,0.0002525037,0.0006213185,0.992269,0.0005707074,0.006139584],"study_design_scores_gemma":[0.000006731503,0.00002051252,0.0001091803,0.0000176088,0.000003701065,0.0001055871,0.00007436091,0.004036166,0.001885151,0.9642118,0.02951538,0.00001383336],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1254882,0.0009455523,0.5969092,0.00112414,0.001085961,0.0002439223,0.0006286781,0.001115333,0.2724591],"genre_scores_gemma":[0.746196,0.0009465489,0.1886714,0.0006366952,0.0003466916,0.0003702792,0.0005365825,0.0005119022,0.06178396],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01099122,"threshold_uncertainty_score":0.03676927,"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."}}