{"id":"W1863544524","doi":"10.1016/j.ejc.2016.01.002","title":"On inversion sets and the weak order in Coxeter groups","year":2016,"lang":"en","type":"article","venue":"European Journal of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Coxeter group; Mathematics; Joins; Inversion (geology); Longest element of a Coxeter group; Coxeter complex; Combinatorics; Point group; Coxeter element; Pure mathematics; Artin group","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":[0.001514441,0.001293505,0.001237857,0.003489652,0.003519144,0.00531646,0.001520849,0.001791428,0.009723484],"category_scores_gemma":[0.004048429,0.0007215566,0.001275467,0.002593927,0.008012096,0.01004638,0.004756913,0.005199961,0.001025128],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002068677,"about_ca_system_score_gemma":0.0008687683,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001938749,"about_ca_topic_score_gemma":0.002067855,"domain_scores_codex":[0.9990632,0.0002800705,0.00005925957,0.0001344458,0.0002184745,0.0002445468],"domain_scores_gemma":[0.997411,0.001517576,0.0002748097,0.000248146,0.0002251106,0.0003234756],"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":[0.00004182272,0.00002337823,0.0002436704,0.00002368785,0.00000495998,0.00006019445,0.0003238382,0.0003842839,0.0002800663,0.9957125,0.0004521914,0.002449434],"study_design_scores_gemma":[0.00001120326,0.00001302306,0.00017812,0.0000115473,0.00000562786,0.00004080146,0.0001445193,0.0006600996,0.0001337646,0.9975024,0.001290449,0.000008353441],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6430157,0.003653566,0.08819581,0.007288139,0.001277611,0.00009028556,0.0004886049,0.0002341588,0.2557561],"genre_scores_gemma":[0.9572101,0.002071799,0.008851711,0.0006801057,0.001196559,0.00008792207,0.0004562901,0.0001000487,0.02934551],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009723484,"threshold_uncertainty_score":0.03252828,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02259396256635644,"score_gpt":0.2625315394824732,"score_spread":0.2399375769161167,"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."}}