{"id":"W4415816767","doi":"10.1007/s00454-025-00762-1","title":"External Columns and Chambers of Vector Partition Functions","year":2025,"lang":"en","type":"article","venue":"Discrete & Computational Geometry","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"Universidad de Sevilla","keywords":"Partition (number theory); Enumeration; Partition function (quantum field theory); Binomial coefficient; Piecewise; Function (biology); Generating function; Vector field","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":[0.0004710765,0.0003168632,0.0003571869,0.000945375,0.00077065,0.002029051,0.000467673,0.0003186214,0.00679844],"category_scores_gemma":[0.001950224,0.0002997069,0.000328515,0.0007931836,0.001540489,0.001931047,0.001323487,0.0006916344,0.0005239489],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007594534,"about_ca_system_score_gemma":0.0003343302,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000862464,"about_ca_topic_score_gemma":0.001015548,"domain_scores_codex":[0.9994654,0.0001094756,0.00002279828,0.00009163975,0.0001528655,0.0001578886],"domain_scores_gemma":[0.9988149,0.0004512859,0.0001801917,0.0001293798,0.000210845,0.0002134069],"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":[0.00007630402,0.00002761156,0.001818107,0.00003984591,0.000006054493,0.0001059255,0.0001844474,0.003937204,0.006628833,0.9785697,0.0006878701,0.007917996],"study_design_scores_gemma":[0.00004611009,0.0001296571,0.004839761,0.00006997476,0.00002856544,0.0005291923,0.0004653717,0.1040367,0.02931249,0.844329,0.01615346,0.0000597219],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8329916,0.0002803556,0.135084,0.0002673577,0.00005338562,0.00003434884,0.0002814662,0.0002585297,0.03074894],"genre_scores_gemma":[0.9835473,0.0001022138,0.009203662,0.00004527732,0.00003806956,0.0000274211,0.000191377,0.00008533812,0.006759182],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00679844,"threshold_uncertainty_score":0.02274305,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02242537675983183,"score_gpt":0.3152630986813809,"score_spread":0.292837721921549,"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."}}