{"id":"W4295180242","doi":"10.54550/eca2023v3s1r1","title":"Combinatorics of triangular partitions","year":2022,"lang":"en","type":"article","venue":"Enumerative Combinatorics and Applications","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Combinatorics; Enumeration; Mathematics; Partition (number theory); Hexagonal lattice; Planar; Line segment; Discrete mathematics; Lattice (music); Geometry; Computer science","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004138005,0.0001985504,0.0003931939,0.0001287477,0.0007772365,0.00002319045,0.0003012098,0.00005022367,0.0001101621],"category_scores_gemma":[0.0002135664,0.0002184271,0.00009000201,0.0008771722,0.0001262532,0.00009562591,0.0003151809,0.0003250255,0.000004406109],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001214822,"about_ca_system_score_gemma":0.00007160317,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003864043,"about_ca_topic_score_gemma":4.235942e-7,"domain_scores_codex":[0.9983808,0.0001480253,0.0005151328,0.0003074559,0.0004187399,0.0002298514],"domain_scores_gemma":[0.9980286,0.0007243584,0.000377957,0.0005210852,0.0002354207,0.0001125728],"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":[0.000005991958,0.000735039,0.0001181159,0.00005292294,0.00003724126,0.000001302685,0.0004620248,0.00002679113,0.0003027269,0.9968092,0.001183965,0.000264617],"study_design_scores_gemma":[0.0008217763,0.000165423,0.00003039883,0.000006938139,0.00005539,0.000008575638,0.0006664194,0.0001557869,0.001440919,0.957777,0.03866326,0.0002080937],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3913186,0.005929902,0.5128978,0.003311683,0.003543173,0.01271648,0.001385672,0.001314076,0.0675826],"genre_scores_gemma":[0.9959678,0.00005550068,0.00192702,0.00003097274,0.00004333413,0.0010736,0.00002593839,0.00004210886,0.000833747],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6046491,"threshold_uncertainty_score":0.89072,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03665745580245052,"score_gpt":0.3172899713760672,"score_spread":0.2806325155736167,"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."}}