{"id":"W1867332349","doi":"10.5539/jmr.v7n4p26","title":"Pairs of Comparable Relations for Complete Homogeneous Symmetric Polynomial","year":2015,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Combinatorics; Homogeneous; Binomial coefficient; Symmetric polynomial; Polynomial; Stirling number; Context (archaeology); Exponential function; Prime (order theory); Elementary symmetric polynomial; Stirling numbers of the second kind; Generating function; Discrete mathematics; Matrix polynomial; Mathematical analysis; Orthogonal polynomials; Difference polynomials","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001365201,0.0005105661,0.0006526292,0.002336367,0.00217805,0.003100519,0.0006252642,0.0008795279,0.01948369],"category_scores_gemma":[0.003222297,0.0003464934,0.000879499,0.001596447,0.002647314,0.005927949,0.002382765,0.002445271,0.002339088],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001049224,"about_ca_system_score_gemma":0.0004501815,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007178929,"about_ca_topic_score_gemma":0.0005821599,"domain_scores_codex":[0.998475,0.0005009567,0.0001013976,0.0003915886,0.0003361324,0.0001949246],"domain_scores_gemma":[0.9985695,0.0005792452,0.0001889961,0.0001828375,0.0003062089,0.0001732195],"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":[0.00001498586,0.000005725179,0.00009952599,0.00002271509,0.00000285429,0.00006120518,0.0001266574,0.00005368605,0.000326781,0.9951633,0.001217962,0.002904583],"study_design_scores_gemma":[0.00001211119,0.00002164112,0.0003642108,0.0000135134,0.000008562571,0.0002019612,0.0001249931,0.0006165468,0.0005131806,0.9881554,0.009954211,0.00001364319],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2181898,0.003679895,0.2264847,0.003119239,0.001472936,0.0002420614,0.001590168,0.0007295568,0.5444916],"genre_scores_gemma":[0.9224509,0.001299977,0.04168768,0.000840552,0.001063733,0.0002027578,0.00131515,0.0002448765,0.03089447],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01948369,"threshold_uncertainty_score":0.06517941,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.512142978547334,"score_gpt":0.4882926991899693,"score_spread":0.02385027935736478,"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."}}