{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006836444,0.0005546435,0.0003948769,0.001638954,0.000678765,0.001565543,0.0007340554,0.0004999724,0.004178617],"category_scores_gemma":[0.003959176,0.0002303037,0.0005012345,0.001087794,0.001878763,0.002352552,0.0009944955,0.0009887975,0.0004087219],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001034091,"about_ca_system_score_gemma":0.000492799,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009445102,"about_ca_topic_score_gemma":0.001071954,"domain_scores_codex":[0.9994572,0.0001161419,0.00001642553,0.00009964438,0.000156406,0.0001541213],"domain_scores_gemma":[0.9973931,0.001348052,0.000369634,0.0002012826,0.0003669984,0.0003208057],"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":[0.0001457527,0.00004443389,0.002986101,0.0001056597,0.00002191611,0.0002068948,0.0002111093,0.008902956,0.01187545,0.9511487,0.001978874,0.02237199],"study_design_scores_gemma":[0.00002537762,0.00008420315,0.003356891,0.00003682642,0.00003285001,0.0006189529,0.0002365728,0.07878333,0.01217796,0.9003621,0.004247367,0.00003744975],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8207346,0.0004760366,0.1248462,0.0004896253,0.00006693116,0.00004084048,0.0002159771,0.0001402989,0.05298937],"genre_scores_gemma":[0.9874759,0.0002210929,0.00693677,0.00009258385,0.00004083271,0.00003095441,0.0001215483,0.00003735036,0.005043023],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004178617,"threshold_uncertainty_score":0.01397884,"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."}}