{"id":"W2147161887","doi":"10.37236/1909","title":"Generating Function for $K$-Restricted Jagged Partitions","year":2005,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":28,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Combinatorics; Mathematics; Lambda; Partition (number theory); Generalization; Generating function; Interpretation (philosophy); Discrete mathematics; Physics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008350382,0.0005550975,0.0006372277,0.001698178,0.001502055,0.001874046,0.001334057,0.0007328801,0.005451358],"category_scores_gemma":[0.003025363,0.000380307,0.0008592129,0.001099025,0.002023789,0.002930845,0.0019737,0.001568516,0.001280694],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001016133,"about_ca_system_score_gemma":0.0004888251,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004550423,"about_ca_topic_score_gemma":0.0006112436,"domain_scores_codex":[0.9993049,0.0001393876,0.00004581813,0.0001434555,0.0001930432,0.0001734043],"domain_scores_gemma":[0.9987657,0.0004645149,0.0002050745,0.0001980961,0.0001839779,0.0001826738],"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":[0.00003274698,0.00001881852,0.0003320152,0.0000335117,0.000004783956,0.0001657925,0.0002239276,0.001795282,0.002399447,0.9881721,0.0006367138,0.006184801],"study_design_scores_gemma":[0.00002371823,0.00004327523,0.0005653315,0.00002567428,0.00001662814,0.0006500727,0.00009266425,0.02313191,0.004780911,0.9635687,0.007053166,0.00004789867],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.66967,0.0005300018,0.2442783,0.0008420852,0.0003188959,0.0001137482,0.000316876,0.0003455797,0.08358448],"genre_scores_gemma":[0.9469753,0.00028386,0.03399786,0.0001950331,0.0002519789,0.0001726163,0.000291571,0.0001452663,0.01768649],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005451358,"threshold_uncertainty_score":0.01823658,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03064624197582931,"score_gpt":0.3108343208109319,"score_spread":0.2801880788351025,"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."}}