{"id":"W1542673380","doi":"10.37236/4822","title":"Hyperbinary Expansions and Stern Polynomials","year":2015,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Combinatorics; Integer (computer science); Sequence (biology); Polynomial; Class (philosophy); Function (biology); Generating function; Stern; Difference polynomials; Discrete mathematics; Orthogonal polynomials; Mathematical analysis","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":[0.0003584461,0.0003770828,0.0002759184,0.001136602,0.0008172698,0.0009532102,0.0006254743,0.0004994846,0.006480166],"category_scores_gemma":[0.001429176,0.0001580732,0.0003007984,0.0009226469,0.001339718,0.001973051,0.0009857659,0.001359356,0.001149499],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007279727,"about_ca_system_score_gemma":0.0004152427,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005561793,"about_ca_topic_score_gemma":0.0006132793,"domain_scores_codex":[0.9996957,0.00005765727,0.00001076272,0.00005496273,0.00009834544,0.00008274049],"domain_scores_gemma":[0.9995123,0.0001593008,0.0000913175,0.00005222961,0.00007976621,0.0001051954],"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":[0.00002476615,0.00001119009,0.0001207537,0.00001549002,0.000001573009,0.00007021397,0.0001128856,0.001038913,0.002507028,0.9897162,0.0004339033,0.005947112],"study_design_scores_gemma":[0.00001571419,0.00004503165,0.0004899608,0.00002459782,0.000005118874,0.0003167407,0.0001556845,0.0222295,0.003896973,0.9645153,0.008279338,0.00002602397],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6195039,0.00121471,0.2588397,0.001056166,0.0002920603,0.00005599142,0.0002938305,0.0003227847,0.1184208],"genre_scores_gemma":[0.94063,0.0006361158,0.02974034,0.0002781925,0.0001982351,0.00006968682,0.0001635472,0.00009654741,0.02818741],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006480166,"threshold_uncertainty_score":0.02167827,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05986491884891614,"score_gpt":0.321807746312308,"score_spread":0.2619428274633918,"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."}}