{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007810903,0.0001266528,0.0002510766,0.00007945098,0.000257424,0.00004783587,0.0002641648,0.00005485168,0.00002442575],"category_scores_gemma":[0.001464281,0.00008758085,0.0001404513,0.0002877224,0.00004365323,0.0002710063,0.00002595774,0.0004217941,0.000006338461],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003173261,"about_ca_system_score_gemma":0.0002196746,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":4.695181e-7,"about_ca_topic_score_gemma":0.000007641292,"domain_scores_codex":[0.9985294,0.00007683119,0.0005759489,0.00007666348,0.0003171598,0.0004240516],"domain_scores_gemma":[0.9977072,0.0009953246,0.000522099,0.0002026578,0.0005174634,0.00005528804],"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":[0.00003302651,0.0001539369,0.000003241023,0.00002426566,0.00008477488,4.27882e-7,0.0001377301,0.0004109823,0.0009418652,0.9938205,0.004082757,0.000306441],"study_design_scores_gemma":[0.0007764348,0.0003737428,0.000006464199,0.00002703453,0.0001866894,0.00005540566,0.0001664334,0.001541489,0.001651543,0.9891167,0.006002612,0.00009540635],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2017867,0.00158412,0.7930724,0.001919483,0.0004469819,0.0003878588,0.000002293806,0.00006181451,0.0007383851],"genre_scores_gemma":[0.995133,0.0001346913,0.002487958,0.00006646726,0.0004472928,0.00002157186,0.000001126208,0.00003097154,0.001676897],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7933463,"threshold_uncertainty_score":0.3571444,"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."}}