{"id":"W1606804863","doi":"10.1090/crmp/035/19","title":"Convex cones and SAGBI bases of permutation invariants","year":2004,"lang":"en","type":"book-chapter","venue":"CRM proceedings & lecture notes","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"Royal Military College of Canada; Queen's University","funders":"","keywords":"Combinatorics; Mathematics; Invariant (physics); Regular polygon; Polynomial ring; Permutation (music); Ring (chemistry); Permutation group; Order (exchange); Polynomial; Pure mathematics; Geometry; Physics; Mathematical analysis; Chemistry; Mathematical physics","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":[0.0001916165,0.0007919702,0.000583754,0.001460019,0.0008408513,0.003060743,0.0005050693,0.0004439644,0.02002921],"category_scores_gemma":[0.0004446539,0.0003727459,0.0004236422,0.002094094,0.0009597309,0.001548428,0.0006036035,0.001800532,0.00380002],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001014645,"about_ca_system_score_gemma":0.0004860721,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001098529,"about_ca_topic_score_gemma":0.0016034,"domain_scores_codex":[0.9998915,0.00002181261,0.000004585502,0.00002050348,0.00004732585,0.00001428938],"domain_scores_gemma":[0.9998692,0.00003634807,0.00001804641,0.00001671424,0.00003273103,0.00002687346],"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":[0.0000409889,0.00003940312,0.0001266504,0.00005664744,0.00001224547,0.00004284398,0.0001150719,0.001763529,0.001197715,0.9026445,0.03846873,0.05549177],"study_design_scores_gemma":[0.000007555299,0.00001301957,0.000326805,0.00002794489,0.000007331106,0.00004790961,0.00005823893,0.002434543,0.0004031476,0.9356089,0.06105265,0.00001185712],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.05436839,0.0404449,0.1166685,0.005900577,0.006097712,0.00004573273,0.0009956502,0.0009945721,0.7744839],"genre_scores_gemma":[0.4308499,0.02675707,0.05594022,0.001486123,0.007075333,0.0001123637,0.002631919,0.0007905145,0.4743567],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02002921,"threshold_uncertainty_score":0.06700438,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01322399768692253,"score_gpt":0.2088755088114998,"score_spread":0.1956515111245773,"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."}}