{"id":"W1595992363","doi":"10.37236/630","title":"Counting Words by Number of Occurrences of Some Patterns","year":2011,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Binomial coefficient; Combinatorics; Integer (computer science); Binomial (polynomial); Order (exchange); Subfamily; Negative binomial distribution; Discrete mathematics; Statistics","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001698179,0.00022122,0.0006842162,0.00008133511,0.00006404501,0.000009885469,0.0009695746,0.00009851193,0.00005835154],"category_scores_gemma":[0.0006121676,0.0001556661,0.0002098546,0.0003539569,0.0001340921,0.0002804056,0.00009923448,0.0006739814,0.000002838241],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001562439,"about_ca_system_score_gemma":0.0002899082,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001050993,"about_ca_topic_score_gemma":0.000001292928,"domain_scores_codex":[0.9972711,0.0001500477,0.00120168,0.0001079753,0.0007684662,0.000500728],"domain_scores_gemma":[0.9957047,0.0008361022,0.002444923,0.0004163016,0.0005344618,0.00006353149],"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":[0.00005106899,0.0005322862,0.002247611,0.0001713147,0.0001642888,0.000002009684,0.00162192,7.903825e-7,0.0003348212,0.9943651,0.0003537268,0.0001550437],"study_design_scores_gemma":[0.0007616397,0.0004211596,0.00003851316,0.0001850953,0.0001609054,0.00006588444,0.0005981425,0.00001941627,0.02066065,0.976783,0.0001614257,0.0001442028],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9756159,0.001240718,0.02100343,0.00004417682,0.0008798687,0.0001736062,0.000006552855,0.00001722464,0.00101854],"genre_scores_gemma":[0.9990391,0.0004650675,0.000295187,0.000009641202,0.00006853128,0.000002665995,3.950075e-7,0.00003487666,0.00008456926],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02342318,"threshold_uncertainty_score":0.6347879,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03080476269194281,"score_gpt":0.3019295607644836,"score_spread":0.2711247980725408,"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."}}