{"id":"W4392134068","doi":"10.1515/spma-2023-0113","title":"The diameter of the Birkhoff polytope","year":2024,"lang":"en","type":"article","venue":"Special Matrices","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université TÉLUQ; Université Laval","funders":"Fonds de recherche du Québec – Nature et technologies; Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Polytope; Combinatorics; Birkhoff polytope; Mathematical economics; Regular polygon; Geometry; Convex set","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":[0.0009689863,0.0005863153,0.0008885281,0.001577024,0.001048709,0.002908021,0.0008306935,0.000576822,0.009484557],"category_scores_gemma":[0.00368927,0.0004291467,0.0004110791,0.0005665743,0.002089029,0.002738435,0.00164195,0.001531688,0.001227216],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001378987,"about_ca_system_score_gemma":0.0004465941,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002042533,"about_ca_topic_score_gemma":0.0008168318,"domain_scores_codex":[0.9988807,0.0002503889,0.00003964037,0.0002587491,0.0003504761,0.0002200978],"domain_scores_gemma":[0.9966625,0.001625487,0.0003901905,0.0001516042,0.00045349,0.0007168165],"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":[0.0001854554,0.00003470207,0.001400414,0.0001063587,0.00002235895,0.0001348149,0.0002006067,0.01075713,0.003424042,0.9680101,0.004248029,0.01147593],"study_design_scores_gemma":[0.00005398341,0.000183528,0.006344057,0.0000994389,0.00002679386,0.000587412,0.0004178097,0.1512193,0.003650965,0.8166528,0.02068653,0.00007738182],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6370281,0.003517107,0.2257682,0.002053069,0.0003931317,0.00007897349,0.001763009,0.00044262,0.1289558],"genre_scores_gemma":[0.9747894,0.0009479082,0.01180461,0.0001376709,0.0002680368,0.0001030377,0.0007534847,0.00009146056,0.01110431],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009484557,"threshold_uncertainty_score":0.03172898,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02226218370481003,"score_gpt":0.3084088217681156,"score_spread":0.2861466380633056,"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."}}