{"id":"W2949474880","doi":"10.48550/arxiv.1108.2219","title":"Staircase skew Schur functions are Schur P-positive","year":2011,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Skew; Mathematics; Conjecture; Schur decomposition; Schur product theorem; Schur's theorem; Schur's lemma; Eulerian path; Combinatorics; Function (biology); Schur complement; Pure mathematics; Physics; Gegenbauer polynomials; Orthogonal polynomials","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":[0.0007180746,0.0008785224,0.0005138793,0.002050276,0.00127811,0.002808744,0.0007718726,0.0006847613,0.007109651],"category_scores_gemma":[0.004709056,0.0004038912,0.0006609833,0.001429231,0.003024128,0.003277615,0.001218051,0.001150303,0.001391304],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008665811,"about_ca_system_score_gemma":0.0005836049,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006069239,"about_ca_topic_score_gemma":0.0007444758,"domain_scores_codex":[0.9993815,0.0001160152,0.0000325948,0.0001077455,0.0002077101,0.0001544045],"domain_scores_gemma":[0.9976261,0.0009550198,0.0003661115,0.000230203,0.0005418925,0.0002807052],"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":[0.00007878361,0.00002450837,0.0009350893,0.0000479134,0.000008373792,0.0001573659,0.0002300019,0.001582163,0.003357799,0.9753524,0.00112707,0.01709847],"study_design_scores_gemma":[0.000009926777,0.00004985277,0.000695465,0.00002438179,0.00001288237,0.0004910481,0.0001784245,0.01418492,0.005088815,0.9759286,0.003307013,0.00002856902],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7706979,0.0004276053,0.1398148,0.0005211587,0.0002107136,0.00005510429,0.0002005914,0.0002682927,0.08780384],"genre_scores_gemma":[0.9829164,0.0002461877,0.008450636,0.000137742,0.000108924,0.00004795095,0.0001096752,0.00005726687,0.007925056],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007109651,"threshold_uncertainty_score":0.0237841,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1649868363173317,"score_gpt":0.2277820188967133,"score_spread":0.06279518257938155,"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."}}