{"id":"W2019523647","doi":"10.1016/j.crma.2015.01.008","title":"Garside families in Artin–Tits monoids and low elements in Coxeter groups","year":2015,"lang":"en","type":"article","venue":"Comptes Rendus Mathématique","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Coxeter group; Mathematics; Artin group; Coxeter element; Longest element of a Coxeter group; Combinatorics; Group (periodic table); Coxeter complex","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006343545,0.0002194499,0.0004578381,0.000476394,0.00002716888,0.00003475749,0.0001941879,0.0001642194,0.0001403344],"category_scores_gemma":[0.0007189917,0.0002030308,0.00003413603,0.000430678,0.00009076636,0.0001255845,0.0001815627,0.0003008213,0.00009093833],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008603434,"about_ca_system_score_gemma":0.0000489778,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000091093,"about_ca_topic_score_gemma":0.0002998706,"domain_scores_codex":[0.9983467,0.0001592536,0.0006088784,0.0002932778,0.0001935902,0.000398231],"domain_scores_gemma":[0.9989816,0.0003985299,0.0001523305,0.0002849031,0.00004874648,0.0001338997],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001800543,0.001934927,0.6624066,0.00106929,0.0001334365,0.0005464318,0.02322222,0.0001267099,0.001261946,0.2301813,0.058789,0.02014807],"study_design_scores_gemma":[0.006295789,0.0004269402,0.1304681,0.0005588949,0.00003547885,0.0001263071,0.006045821,0.008988473,0.002325457,0.8409133,0.002744212,0.001071234],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9943439,0.0004367606,0.0005096257,0.0003287438,0.0001304334,0.0002898991,0.000006143275,0.00006138538,0.003893049],"genre_scores_gemma":[0.993234,0.00009348255,0.006025568,0.0001621753,0.00003620287,0.00005072998,0.000008133803,0.00002505523,0.0003646003],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.610732,"threshold_uncertainty_score":0.8279356,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04803048959976338,"score_gpt":0.3000910030671327,"score_spread":0.2520605134673693,"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."}}