{"id":"W2964198259","doi":"10.1007/s10801-017-0738-6","title":"Decomposing inversion sets of permutations and applications to faces of the Littlewood–Richardson cone","year":2017,"lang":"en","type":"article","venue":"Journal of Algebraic Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Royal Military College of Canada; Queen's University","funders":"","keywords":"Combinatorics; Mathematics; Disjoint sets; Permutation (music); Tuple; Inversion (geology); Alpha (finance); Discrete mathematics; Physics","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":[0.0005094726,0.0001464687,0.00047611,0.0001363134,0.000318861,0.00004467364,0.0006879686,0.00008202759,0.000005332171],"category_scores_gemma":[0.001830216,0.0001122344,0.0001318146,0.0002252119,0.0001578453,0.0002375069,0.0002989602,0.0002321037,0.000001031405],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008200458,"about_ca_system_score_gemma":0.0001122165,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003915182,"about_ca_topic_score_gemma":0.000002099752,"domain_scores_codex":[0.998418,0.00006380803,0.0007582821,0.000114853,0.0005008771,0.0001441249],"domain_scores_gemma":[0.9958116,0.0007155075,0.002019984,0.0006209972,0.0007139013,0.0001180039],"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":[0.00003200104,0.0005275249,0.002934813,0.0004889048,0.0001263799,0.000002530447,0.002696487,0.00002969662,0.00738694,0.9831041,0.0005912012,0.002079445],"study_design_scores_gemma":[0.0008490023,0.0002017723,0.00263725,0.0003265722,0.0001465672,0.00003123474,0.0005126277,0.0001050908,0.01429555,0.9802875,0.0004866381,0.0001202303],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9876572,0.0002049539,0.009782886,0.0008017804,0.0006366042,0.0004389306,0.00001020878,0.000009423775,0.0004579861],"genre_scores_gemma":[0.9932641,0.00005497812,0.006543003,0.00001706735,0.00004180735,0.000005833717,2.463428e-7,0.00002121278,0.0000517052],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00690861,"threshold_uncertainty_score":0.4576784,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03996779083937365,"score_gpt":0.3468956971321973,"score_spread":0.3069279062928237,"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."}}