{"id":"W4394793213","doi":"10.61091/ars158-11","title":"Prefixes of Stanley’s Catalan Paths with Odd Returns to the \\(x\\)-axis–Standard Version and Skew Catalan-Stanley Paths","year":2024,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"semigroups and automata theory","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Catalan number; Catalan; Combinatorics; Skew; Tuple; Alphabet; Order (exchange); Set (abstract data type); Discrete mathematics; Computer science; Humanities; Telecommunications","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":[0.0009749667,0.0004435293,0.0004939836,0.001478717,0.001443711,0.002337893,0.0006542052,0.0009277689,0.009389831],"category_scores_gemma":[0.00479796,0.000398301,0.0008695522,0.001282121,0.002074017,0.002752803,0.001035002,0.001298967,0.001837979],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001261431,"about_ca_system_score_gemma":0.0008752167,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001143465,"about_ca_topic_score_gemma":0.001435432,"domain_scores_codex":[0.9991897,0.000189678,0.00006013722,0.0001681752,0.0002021234,0.0001901766],"domain_scores_gemma":[0.9974261,0.001157807,0.000264794,0.0004514554,0.0004372375,0.0002626687],"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":[0.00004578576,0.00001456341,0.000401864,0.00002172433,0.00000320071,0.0001849751,0.0002639985,0.001324189,0.001365789,0.9869404,0.0009334477,0.008499946],"study_design_scores_gemma":[0.00001532171,0.00002917886,0.0005956751,0.00002480658,0.000005903536,0.0003606255,0.0001067594,0.01755393,0.002917795,0.9699425,0.008417122,0.00003044181],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5950276,0.0005877871,0.27474,0.0009014514,0.0004303099,0.0001346601,0.0005917495,0.0006600819,0.1269264],"genre_scores_gemma":[0.9009784,0.0002953033,0.06118513,0.0002818234,0.0001733463,0.0002127237,0.0004866134,0.0003729849,0.0360136],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009389831,"threshold_uncertainty_score":0.03141207,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.006239565600843324,"score_gpt":0.2159879738433406,"score_spread":0.2097484082424973,"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."}}