{"id":"W1973203145","doi":"10.1007/s10801-007-0113-0","title":"Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes","year":2007,"lang":"en","type":"article","venue":"Journal of Algebraic Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia; University of Toronto","funders":"","keywords":"Mathematics; Schubert polynomial; Schur algebra; Schur polynomial; Skew; Schur's lemma; Schur's theorem; Combinatorics; Schur decomposition; Schur product theorem; Conjecture; Symmetric function; Pure mathematics; Schur complement; Macdonald polynomials; Orthogonal polynomials; Computer science; Jacobi polynomials; Physics; Classical 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":[0.001713432,0.001020468,0.001378831,0.004507815,0.002422735,0.003450443,0.001299894,0.001538488,0.008170657],"category_scores_gemma":[0.007734403,0.0006789973,0.000945116,0.002775193,0.005138687,0.005907136,0.002692704,0.002839399,0.0007187216],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001525737,"about_ca_system_score_gemma":0.0006140261,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000990689,"about_ca_topic_score_gemma":0.00123911,"domain_scores_codex":[0.9992461,0.0002640517,0.0000407599,0.0001594596,0.0001745279,0.0001151956],"domain_scores_gemma":[0.9965308,0.00177769,0.0004241393,0.0001966741,0.0005015257,0.000569154],"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":[0.00002785101,0.00001367209,0.0001742055,0.00002132035,0.000003487811,0.00006553453,0.0001704846,0.0007459687,0.0007228201,0.9924312,0.0005217207,0.00510164],"study_design_scores_gemma":[0.00000667937,0.00001018502,0.0001467455,0.00001125035,0.000004520337,0.00009400098,0.00007560411,0.004455711,0.0003844994,0.9933901,0.001406527,0.00001424697],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4683943,0.00411635,0.3479531,0.003356733,0.001074077,0.0001008452,0.0002889602,0.0003843479,0.1743312],"genre_scores_gemma":[0.9524508,0.00177618,0.02669824,0.0003987256,0.001002876,0.00006190401,0.0001228855,0.0001465362,0.0173419],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008170657,"threshold_uncertainty_score":0.02733362,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02653940955674833,"score_gpt":0.311838879041383,"score_spread":0.2852994694846346,"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."}}