{"id":"W2165572529","doi":"10.1515/integ.2011.001","title":"Symmetries in Steinhaus Triangles and in Generalized Pascal Triangles","year":2011,"lang":"en","type":"article","venue":"Integers","topic":"Cellular Automata and Applications","field":"Computer Science","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University of Manitoba","keywords":"Homogeneous space; Pascal (unit); Mathematics; Dihedral group; Binary number; Dihedral angle; Combinatorics; Pure mathematics; Algebra over a field; Geometry; Computer science; Physics; Arithmetic; Group (periodic table)","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003406141,0.0002459912,0.0002913453,0.0006946662,0.0009362649,0.001214563,0.0005154381,0.0005689877,0.01093965],"category_scores_gemma":[0.001675263,0.0001993152,0.0003842571,0.0006724105,0.001252992,0.00159548,0.0009002613,0.0006749334,0.001251195],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005128662,"about_ca_system_score_gemma":0.0003619182,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006923335,"about_ca_topic_score_gemma":0.001119057,"domain_scores_codex":[0.9995865,0.00007439843,0.00002808031,0.00005101075,0.0001592447,0.0001007008],"domain_scores_gemma":[0.9996474,0.00009866451,0.00004717696,0.00007316323,0.00008669776,0.00004680732],"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":[0.0000235382,0.00001085745,0.0001405412,0.00002908502,0.000001450147,0.00009517677,0.0001260543,0.002258973,0.003216664,0.9789087,0.0006214668,0.01456748],"study_design_scores_gemma":[0.00003352288,0.00005469281,0.0002723405,0.00002037831,0.000005693645,0.0002685735,0.0002502538,0.02356747,0.01130799,0.9491374,0.01505856,0.00002300894],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5491809,0.0003265212,0.2950777,0.0005812582,0.0003806374,0.0002151964,0.0003321776,0.0005794768,0.1533261],"genre_scores_gemma":[0.9137172,0.0002084001,0.06799333,0.0001578569,0.00005398148,0.000100104,0.0001780736,0.0001391393,0.01745181],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01093965,"threshold_uncertainty_score":0.03659678,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03611765041715627,"score_gpt":0.234303913910352,"score_spread":0.1981862634931957,"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."}}