{"id":"W2948592123","doi":"10.37236/8935","title":"A Combinatorial Model for the Decomposition of Multivariate Polynomial Rings as $S_n$-Modules","year":2020,"lang":"en","type":"preprint","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Partition (number theory); Multiset; Lambda; Invariant (physics); Multiplicity (mathematics); Combinatorics; Polynomial ring; Ring (chemistry); Polynomial; Discrete mathematics; Physics; Mathematical analysis","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","research_integrity"],"consensus_categories":[],"category_scores_codex":[0.002932038,0.0007270649,0.00167926,0.0001800298,0.0003763189,0.0001186222,0.002873066,0.0005093844,0.000004855948],"category_scores_gemma":[0.00306389,0.0004820798,0.001064655,0.0003564181,0.0002393309,0.0001898343,0.0009109841,0.00322389,0.000002648517],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009864679,"about_ca_system_score_gemma":0.001884068,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001734437,"about_ca_topic_score_gemma":0.000003430762,"domain_scores_codex":[0.9948344,0.0003493424,0.002169423,0.0004085955,0.001308237,0.0009299631],"domain_scores_gemma":[0.9879994,0.004573807,0.004721248,0.001141154,0.001389893,0.0001745196],"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":[0.001020881,0.00055568,0.000001819364,0.0004988657,0.0009487674,0.000003697213,0.001951984,0.004274247,0.0008787779,0.988677,0.001022538,0.0001657769],"study_design_scores_gemma":[0.003691285,0.0009537518,0.000002916496,0.0003160637,0.001284641,0.00006349503,0.0001528155,0.0779532,0.004018111,0.9107364,0.0004189437,0.0004083132],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1064462,0.002646675,0.8747929,0.004012977,0.008599698,0.003052111,0.00004615969,0.0001082622,0.0002949509],"genre_scores_gemma":[0.9956849,0.0005145379,0.0024169,0.00006175551,0.000956865,0.00009290053,0.000005924909,0.0001824258,0.00008381493],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8892387,"threshold_uncertainty_score":0.9997631,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04223306576836299,"score_gpt":0.351274159550569,"score_spread":0.309041093782206,"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."}}