{"id":"W4414596675","doi":"10.1007/s00454-025-00770-1","title":"Combinatorics of Generalized Parking-Function Polytopes","year":2025,"lang":"lv","type":"article","venue":"Discrete & Computational Geometry","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"University of Wyoming; Harvey Mudd College; National Science Foundation","keywords":"Polytope; Convex hull; Sequence (biology); Regular polygon; Convex polytope; Chain (unit)","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003876838,0.0006440946,0.0008683933,0.001619531,0.001499983,0.003402942,0.000988126,0.0006204442,0.02765782],"category_scores_gemma":[0.0009694406,0.0004557347,0.001179052,0.001618721,0.002032684,0.002422348,0.001851678,0.001349786,0.003116193],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00157939,"about_ca_system_score_gemma":0.0005955703,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001842052,"about_ca_topic_score_gemma":0.002215548,"domain_scores_codex":[0.999454,0.0001068986,0.00003053859,0.0001155814,0.000141171,0.0001518836],"domain_scores_gemma":[0.9995095,0.0001754489,0.00005969908,0.00006473497,0.00007703482,0.0001135511],"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":[0.00002898263,0.00002021125,0.0001526459,0.00006505651,0.00001375773,0.000147952,0.000082276,0.0028225,0.0003398556,0.9873782,0.00328031,0.005668267],"study_design_scores_gemma":[0.00003768559,0.00002140023,0.0003313596,0.00002517594,0.00001547496,0.0002358998,0.0001585842,0.00932095,0.0005029139,0.9758098,0.01352037,0.00002043602],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5024148,0.001223388,0.1369656,0.002108132,0.0005151673,0.000124958,0.001386129,0.0008098071,0.3544521],"genre_scores_gemma":[0.929873,0.0005567066,0.01357759,0.0002722534,0.0001685173,0.0001040918,0.0009754929,0.0001740682,0.05429823],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02765782,"threshold_uncertainty_score":0.09252471,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01800016506785492,"score_gpt":0.3081994212894893,"score_spread":0.2901992562216344,"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."}}