{"id":"W1930520427","doi":"10.37236/4971","title":"Tokuyama's Identity for Factorial Schur $P$ and $Q$ Functions","year":2015,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"Wilfrid Laurier University","funders":"Banff International Research Station for Mathematical Innovation and Discovery; Natural Sciences and Engineering Research Council of Canada; Wilfrid Laurier University","keywords":"Mathematics; Vandermonde matrix; Combinatorics; Factorial; Partition (number theory); Identity (music); Product (mathematics); Lattice (music); Vertex (graph theory); Extension (predicate logic); Mathematical analysis; Graph; Geometry; Computer science","routes":{"ca_aff":true,"ca_fund":true,"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":[0.00233175,0.0002008252,0.0004362986,0.00009983851,0.0001919606,0.0000850461,0.0005001561,0.0001055414,0.000003769412],"category_scores_gemma":[0.003396222,0.0001415608,0.000150485,0.0003052736,0.00008032739,0.0005200376,0.0000971562,0.0006068173,0.000003890478],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004856224,"about_ca_system_score_gemma":0.0005619957,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002172636,"about_ca_topic_score_gemma":0.000005664474,"domain_scores_codex":[0.9980375,0.0001168107,0.000610504,0.0001245032,0.0006090371,0.0005016609],"domain_scores_gemma":[0.9967287,0.001228203,0.000686725,0.0003300095,0.0008556166,0.0001707258],"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":[0.0001262428,0.0001578659,0.00003502214,0.00003246079,0.0001097455,0.000001432494,0.0003969762,0.000007379714,0.00007256102,0.9953482,0.003567975,0.0001441229],"study_design_scores_gemma":[0.002553308,0.0009549975,0.000006985892,0.00002412534,0.0002061471,0.0001317632,0.0004611835,0.00006489386,0.0003210364,0.983117,0.01200901,0.000149512],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3055877,0.002111066,0.682797,0.0008483635,0.007119725,0.0006967598,0.000005500769,0.00006786428,0.0007660216],"genre_scores_gemma":[0.9978917,0.0001149603,0.0006724995,0.00002038055,0.0007176438,0.00001267593,6.385251e-7,0.00004362678,0.0005258396],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6923041,"threshold_uncertainty_score":0.5772682,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06856880706982962,"score_gpt":0.3496635254170486,"score_spread":0.281094718347219,"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."}}