{"id":"W4281651995","doi":"10.54550/eca2022v2s3r21","title":"The Gröbner basis of a Catalan path ideal","year":2022,"lang":"en","type":"article","venue":"Enumerative Combinatorics and Applications","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Combinatorics; Diagonal; Basis (linear algebra); Quotient; Dimension (graph theory); Ideal (ethics); Quotient ring; Intersection (aeronautics); Order (exchange); Young tableau; General linear group; Discrete mathematics; Polynomial ring; Symmetric group; Geometry; Mathematical analysis; Polynomial","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0002243571,0.0002554763,0.0002429672,0.0006894647,0.0006662551,0.001132944,0.0004405176,0.000265337,0.00681064],"category_scores_gemma":[0.0003185078,0.0001505665,0.0002669333,0.0003809677,0.001145172,0.0008272463,0.0007766626,0.000747614,0.001635848],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008758511,"about_ca_system_score_gemma":0.0008196739,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00183177,"about_ca_topic_score_gemma":0.00170965,"domain_scores_codex":[0.9997738,0.00002817931,0.000006910665,0.00004598908,0.00007196224,0.00007314723],"domain_scores_gemma":[0.9998761,0.00002362322,0.00001659276,0.00001654077,0.00003090142,0.00003620896],"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":[0.00006459336,0.00003294038,0.0003972257,0.00005021625,0.000005334459,0.0001336953,0.0002695261,0.002338793,0.009462949,0.9751412,0.00166276,0.01044083],"study_design_scores_gemma":[0.00005088097,0.0001049394,0.001984209,0.00003185708,0.00001367597,0.0002968216,0.000192259,0.01548483,0.00979509,0.9450283,0.02697766,0.00003947975],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7782551,0.0006001848,0.07810406,0.0009555109,0.000169687,0.0001149232,0.001276096,0.0003600283,0.1401644],"genre_scores_gemma":[0.9543117,0.0002423385,0.01798427,0.000170973,0.00009425371,0.00006485064,0.0007873634,0.00004806054,0.02629599],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00681064,"threshold_uncertainty_score":0.02278382,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02272212294432134,"score_gpt":0.2950282351225474,"score_spread":0.2723061121782261,"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."}}