{"id":"W4415667515","doi":"10.55016/ojs/cdm.v20i2.79510","title":"Fibonacci numbers and n-color compositions","year":2025,"lang":"","type":"article","venue":"Contributions to Discrete Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Fibonacci number; Bijection; Rectangle; Composition (language); Tile; Type (biology); Generating function","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"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":[0.0007496646,0.0005118321,0.000447594,0.0009434862,0.001461584,0.001248875,0.0004742138,0.0008101822,0.003173594],"category_scores_gemma":[0.002552752,0.0003697646,0.0006876919,0.0009277911,0.002690445,0.002275705,0.001050161,0.001316553,0.0004796285],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00125856,"about_ca_system_score_gemma":0.0006472887,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001207244,"about_ca_topic_score_gemma":0.001458367,"domain_scores_codex":[0.9993933,0.0001893255,0.00004207476,0.0001331981,0.0001651625,0.00007697226],"domain_scores_gemma":[0.9987865,0.0007460843,0.0001202152,0.0001317332,0.0001255903,0.00008987298],"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":[0.00005210943,0.0000163881,0.0003642204,0.00004604733,0.000006236572,0.00006844974,0.0001781951,0.006384253,0.002787529,0.9742338,0.0007756631,0.01508717],"study_design_scores_gemma":[0.00002221788,0.00003969948,0.0007875552,0.00002208989,0.00001138177,0.0002982039,0.000102572,0.02274714,0.003026404,0.9592485,0.01366548,0.00002871409],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4302093,0.004064132,0.4251776,0.001559932,0.0005338197,0.0001200659,0.0001701373,0.0002194476,0.1379456],"genre_scores_gemma":[0.8479404,0.001472758,0.1272733,0.0004574291,0.0002777117,0.0002305112,0.0001510291,0.00007121915,0.02212558],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003173594,"threshold_uncertainty_score":0.01061672,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01062308119312045,"score_gpt":0.347479074236419,"score_spread":0.3368559930432986,"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."}}