{"id":"W1981946205","doi":"10.1006/aama.2001.0736","title":"Random Partitions with Non-negative rth Differences","year":2001,"lang":"en","type":"article","venue":"Advances in Applied Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":17,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Mathematics; Combinatorics; Partition (number theory); Bijection; Omega; Integer (computer science); Discrete mathematics","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":[0.007535164,0.001138569,0.002181572,0.003186767,0.001693749,0.005018914,0.002982745,0.00337628,0.0125364],"category_scores_gemma":[0.03771499,0.001311865,0.001293683,0.001365374,0.00690597,0.008419146,0.004888104,0.004125391,0.002268857],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001725885,"about_ca_system_score_gemma":0.0009158987,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003514388,"about_ca_topic_score_gemma":0.0003619822,"domain_scores_codex":[0.9945088,0.002539937,0.0002124358,0.0009041418,0.001175691,0.000658929],"domain_scores_gemma":[0.9696572,0.01942289,0.002928048,0.004350849,0.001622403,0.002018594],"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":[0.00009852931,0.00002348298,0.0002200576,0.00003425683,0.00001462874,0.00006670578,0.00008887522,0.003249259,0.0007210608,0.9919004,0.0007993302,0.002783376],"study_design_scores_gemma":[0.0000672644,0.0000442791,0.0003435369,0.00002714286,0.00001178071,0.0002401223,0.00005526348,0.04870962,0.0008190685,0.9483317,0.001307284,0.00004295346],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2432554,0.001319696,0.7230696,0.002784966,0.0006719318,0.0002572769,0.0006024668,0.000686185,0.02735258],"genre_scores_gemma":[0.8963568,0.0007745899,0.06650985,0.000943379,0.0008010837,0.0004724432,0.0005312219,0.0003748865,0.03323577],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.0125364,"threshold_uncertainty_score":0.04193848,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02686189053724694,"score_gpt":0.3081751111392917,"score_spread":0.2813132206020448,"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."}}