{"id":"W4386351978","doi":"10.1016/j.jcta.2023.105803","title":"Constructing uniform 2-factorizations via row-sum matrices: Solutions to the Hamilton-Waterloo problem","year":2023,"lang":"en","type":"article","venue":"Journal of Combinatorial Theory Series A","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"Toronto Metropolitan University; University of New Brunswick","funders":"Agencia Nacional de Promoción Científica y Tecnológica; Natural Sciences and Engineering Research Council of Canada; Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni; Agencia Nacional de Promoción de la Investigación, el Desarrollo Tecnológico y la Innovación; Universidad Nacional de San Luis; Istituto Nazionale di Alta Matematica \"Francesco Severi\"","keywords":"Dihedral group; Mathematics; Combinatorics; Cayley graph; Factorization; Abelian group; Group (periodic table); Matrix (chemical analysis); Construct (python library); Spectrum (functional analysis); Discrete mathematics; Computer science; Algorithm; Graph","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":[0.001651001,0.0001992577,0.0003148593,0.0002736245,0.0004180284,0.0001413974,0.0004555711,0.0001021189,0.00005186719],"category_scores_gemma":[0.00009665851,0.0001436546,0.0001694212,0.001112468,0.00008914566,0.0004818166,0.0000595132,0.0003422926,0.00005816772],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001056845,"about_ca_system_score_gemma":0.00004951091,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004926742,"about_ca_topic_score_gemma":0.00000999421,"domain_scores_codex":[0.9983404,0.00020198,0.0006497985,0.0001013362,0.0003105601,0.0003959612],"domain_scores_gemma":[0.998887,0.0002825691,0.0002023607,0.0002540653,0.0002261333,0.0001478612],"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":[0.0001121133,0.00002223198,0.0001266755,0.00007119165,0.000213801,0.00001789135,0.004414327,0.008485109,0.001658132,0.9815507,0.002192891,0.001134972],"study_design_scores_gemma":[0.001053442,0.0004167274,0.00009161789,0.0002642681,0.0001380682,0.000444292,0.01459268,0.0006008148,0.003530991,0.8731906,0.1052057,0.0004707374],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8601434,0.0009035937,0.04680852,0.001458744,0.06847076,0.001566639,0.0001448213,0.00134073,0.0191628],"genre_scores_gemma":[0.9982892,0.00007633273,0.0002052028,0.00001997601,0.0009610498,0.0000188861,0.000006285231,0.00004453585,0.0003785725],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1381458,"threshold_uncertainty_score":0.5858063,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.00954778292910096,"score_gpt":0.2026864869044561,"score_spread":0.1931387039753551,"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."}}