{"id":"W3001604198","doi":"10.1137/20m1320730","title":"Counting Linear Extensions of Posets with Determinants of Hook Lengths","year":2021,"lang":"en","type":"preprint","venue":"SIAM Journal on Discrete Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"International Max Planck Research School for Advanced Methods in Process and Systems Engineering; Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs; National Science Foundation","keywords":"Mathematics; Combinatorics; Skew; Hook; Ribbon; Star product; Descent (aeronautics); Class (philosophy); Discrete mathematics; Geometry; Computer science; Physics","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":[0.001476051,0.0009191727,0.002843332,0.0004032459,0.000188631,0.0001161166,0.001111895,0.0005501595,0.00009474839],"category_scores_gemma":[0.004036618,0.0007004707,0.0007018003,0.0003602358,0.0002994461,0.0002093134,0.0008838709,0.002036498,0.000006813659],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001788234,"about_ca_system_score_gemma":0.0006762364,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003518469,"about_ca_topic_score_gemma":0.000009400012,"domain_scores_codex":[0.993577,0.0002228123,0.003065612,0.0005418265,0.001944006,0.0006487662],"domain_scores_gemma":[0.9878958,0.002179628,0.006112012,0.001883343,0.001646926,0.0002822913],"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":[0.001805834,0.02437058,0.002602705,0.1666387,0.009795543,0.005940718,0.07838371,0.01393736,0.01616002,0.6705721,0.002548437,0.007244273],"study_design_scores_gemma":[0.002244983,0.001202665,0.00006606288,0.04094285,0.00152547,0.001349763,0.005881941,0.01153905,0.02976844,0.9039184,0.00005851728,0.001501883],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9543399,0.0003589308,0.04069418,0.00008168678,0.001109932,0.001084264,0.0001168299,0.00009586111,0.002118453],"genre_scores_gemma":[0.6015213,0.0002724227,0.3974222,0.00002114259,0.0002341113,0.00002341285,0.00001035072,0.0002700968,0.0002249215],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.356728,"threshold_uncertainty_score":0.9995446,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04490005041821215,"score_gpt":0.3455230302338493,"score_spread":0.3006229798156371,"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."}}