{"id":"W2085334526","doi":"10.1016/s0304-3975(03)00220-2","title":"Two bijective proofs for the arborescent form of the Good–Lagrange formula and some applications to colored rooted trees and cacti","year":2003,"lang":"en","type":"article","venue":"Theoretical Computer Science","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Colored; Mathematical proof; Mathematics; Bijection; Combinatorics; Polyomino; Algebra over a field; Discrete mathematics; Pure mathematics; Geometry","routes":{"ca_aff":true,"ca_fund":false,"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":[0.002870956,0.001296538,0.001032383,0.003298285,0.00360177,0.00435553,0.002821606,0.002550695,0.01759718],"category_scores_gemma":[0.01396025,0.00120661,0.002152122,0.004243179,0.004583958,0.01118117,0.005210293,0.009189161,0.00207222],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002250099,"about_ca_system_score_gemma":0.001201219,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001170416,"about_ca_topic_score_gemma":0.002248577,"domain_scores_codex":[0.9983605,0.0004717056,0.0001282464,0.0002629356,0.0005879194,0.000188676],"domain_scores_gemma":[0.9933518,0.003949502,0.0003946143,0.0008909167,0.0009854835,0.0004277185],"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":[0.00001139388,0.00002735538,0.00008400559,0.00005484755,0.000006144934,0.00008532637,0.0001955623,0.0002432784,0.0004324596,0.987194,0.003338823,0.008326819],"study_design_scores_gemma":[0.00001503955,0.00001205414,0.0001330341,0.00002841892,0.00001747831,0.000169922,0.00006077713,0.002236096,0.0008589802,0.98532,0.01112095,0.00002705883],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04104575,0.001994966,0.8063367,0.008159383,0.001868286,0.0001713351,0.0005717796,0.0007534431,0.1390984],"genre_scores_gemma":[0.5000313,0.0038589,0.4092493,0.00453953,0.003062272,0.0005081596,0.001121733,0.001241645,0.07638721],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01759718,"threshold_uncertainty_score":0.05886841,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02087328041120082,"score_gpt":0.3137634951874374,"score_spread":0.2928902147762366,"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."}}