{"id":"W2911019483","doi":"10.37236/8930","title":"Schur and $e$-Positivity of Trees and Cut Vertices","year":2020,"lang":"en","type":"preprint","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia; University of Toronto","funders":"","keywords":"Combinatorics; Mathematics; Vertex (graph theory); Bipartite graph; Symmetric function; Graph; Chromatic scale; Discrete mathematics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001393115,0.0003759908,0.001129327,0.000120707,0.0001049524,0.00006429695,0.0007038975,0.0002329407,0.000002352636],"category_scores_gemma":[0.001443627,0.0002731918,0.0001809905,0.0002117048,0.0002236147,0.000151523,0.0007421676,0.00202556,4.96546e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002103448,"about_ca_system_score_gemma":0.0005234486,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004541238,"about_ca_topic_score_gemma":0.00001020681,"domain_scores_codex":[0.997427,0.0002898519,0.0009634545,0.0002286726,0.0006549588,0.000436017],"domain_scores_gemma":[0.9953576,0.001679858,0.001946263,0.0004754761,0.000402889,0.0001378795],"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":[0.0001193162,0.0002030692,0.0001306891,0.0006825941,0.0003974253,0.00001048071,0.001090592,0.00001089138,0.0005132983,0.9963402,0.0001783718,0.0003230547],"study_design_scores_gemma":[0.000967128,0.000725785,0.000130974,0.0003864137,0.000620737,0.0001390035,0.0002118722,0.0002483481,0.002919784,0.9932723,0.000143958,0.0002337048],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9684066,0.01208179,0.01607702,0.001559904,0.0008658331,0.0004887346,0.000007228779,0.00003779982,0.000475062],"genre_scores_gemma":[0.9959715,0.003298807,0.0004779193,0.00002039736,0.0001325663,0.000004828228,5.260001e-7,0.00005522407,0.00003825783],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02756485,"threshold_uncertainty_score":0.999972,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03273519531832711,"score_gpt":0.3073279269561024,"score_spread":0.2745927316377753,"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."}}