{"id":"W4390712995","doi":"10.55016/ojs/cdm.v18i1.73025","title":"On a generalized basic series and Rogers-Ramanujan type identities","year":2023,"lang":"en","type":"article","venue":"Contributions to Discrete Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"University Grants Commission","keywords":"Mathematics; Bijection; Combinatorics; Type (biology); Ramanujan theta function; Combinatorial proof; Generating function; Series (stratigraphy); Ramanujan's sum; Generalization; Class (philosophy); Ramanujan tau function; Combinatorial principles; Discrete mathematics; Combinatorial explosion; Computer science","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001007272,0.0006254137,0.0005103959,0.001486359,0.001118914,0.001646158,0.0009026225,0.0007678202,0.004895598],"category_scores_gemma":[0.001442675,0.0002227033,0.0008798502,0.0009721604,0.002626944,0.0036542,0.001526437,0.001412683,0.001131094],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007248247,"about_ca_system_score_gemma":0.0004214493,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004178569,"about_ca_topic_score_gemma":0.0003678897,"domain_scores_codex":[0.9994517,0.0001414803,0.00002859585,0.00009458493,0.0001986377,0.00008507998],"domain_scores_gemma":[0.9995958,0.0001210217,0.00005397157,0.0000842114,0.00008143226,0.00006365097],"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":[0.000003753591,0.000004583854,0.00003549305,0.00001076551,0.000001069214,0.00005903153,0.00007208654,0.0003630451,0.0005786881,0.9963487,0.0002606275,0.002261964],"study_design_scores_gemma":[0.000005794993,0.00001571068,0.0001173554,0.00001121074,0.000003582271,0.0002928277,0.00004650907,0.004052092,0.0005978598,0.9871733,0.007670971,0.00001282039],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.3840576,0.002550925,0.2459459,0.001514821,0.00133256,0.00009846649,0.0001956386,0.0003453802,0.3639588],"genre_scores_gemma":[0.8932136,0.00159215,0.05126929,0.0005973449,0.0008999705,0.0001045648,0.0001325039,0.0001264187,0.05206418],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004895598,"threshold_uncertainty_score":0.01637739,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03593593663408055,"score_gpt":0.354398821264493,"score_spread":0.3184628846304124,"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."}}