{"id":"W1616478863","doi":"10.37236/585","title":"Counting the Number of Elements in the Mutation Classes of $\\tilde A_n-$Quivers","year":2011,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Quiver; Mathematics; Cluster algebra; Type (biology); Equivalence (formal languages); Tilde; Combinatorics; Product (mathematics); Pure mathematics; Geometry; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002481308,0.000139237,0.0003062531,0.00005659854,0.00009759906,0.00001444116,0.0008901725,0.00006730467,0.00003118566],"category_scores_gemma":[0.0002943919,0.0000689305,0.0001503707,0.000393892,0.0001096875,0.0001254775,0.00005229506,0.0005874747,7.590385e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001352202,"about_ca_system_score_gemma":0.0002645339,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004554659,"about_ca_topic_score_gemma":0.000009490656,"domain_scores_codex":[0.9978257,0.0003176725,0.0007734256,0.00007577268,0.0006705979,0.0003367992],"domain_scores_gemma":[0.9973256,0.0007404919,0.001298244,0.0003086224,0.0003078495,0.0000192209],"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":[0.00008215808,0.0001503746,0.002012913,0.00002603329,0.0001107203,0.000002341465,0.004829751,0.000007664098,0.00005036841,0.992482,0.0001034073,0.0001422817],"study_design_scores_gemma":[0.0008476769,0.0002567228,0.001562307,0.00004387274,0.0001393059,0.00007482881,0.003017519,0.00004898496,0.001338665,0.9925051,0.00009612749,0.00006892137],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9963766,0.0004068763,0.001002944,0.0001645117,0.0004153298,0.0002006639,5.163199e-7,0.000003877415,0.001428619],"genre_scores_gemma":[0.9996403,0.0001806171,0.00004734057,0.00003749879,0.00005361568,0.000002975312,2.312382e-7,0.00001550608,0.00002195769],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003263596,"threshold_uncertainty_score":0.2810904,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03247813008759766,"score_gpt":0.296360763325456,"score_spread":0.2638826332378584,"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."}}