{"id":"W2551475233","doi":"10.46298/dmtcs.2503","title":"Negative $q$-Stirling numbers","year":2015,"lang":"en","type":"article","venue":"Discrete Mathematics & Theoretical Computer Science","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"National Security Agency; Princeton University; Simons Foundation","keywords":"Mathematics; Stirling numbers of the first kind; Stirling number; Partially ordered set; Combinatorics; Binomial coefficient; Stirling numbers of the second kind; Binomial (polynomial); Bijection; Statistics","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":[0.0005863914,0.000535474,0.0004249425,0.001850162,0.001104495,0.002130826,0.0005065512,0.0005155258,0.007594835],"category_scores_gemma":[0.002697336,0.000292764,0.0005201964,0.0009575001,0.003165412,0.003346941,0.001281886,0.001472326,0.001550961],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000934572,"about_ca_system_score_gemma":0.0005309747,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005376122,"about_ca_topic_score_gemma":0.0006896585,"domain_scores_codex":[0.9992919,0.0001110169,0.00003385779,0.0001774397,0.000244427,0.0001413592],"domain_scores_gemma":[0.9990778,0.0003402401,0.0001437894,0.00008542125,0.0002108989,0.0001418879],"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":[0.00002178635,0.000005351077,0.0004647984,0.00002757548,0.000002092552,0.00007188808,0.0001382551,0.0005363817,0.00196704,0.9876255,0.001016529,0.008122757],"study_design_scores_gemma":[0.000008519919,0.00005756078,0.0009314235,0.00003986351,0.000008032865,0.0006498565,0.0002164562,0.006938209,0.004262077,0.9541463,0.03269627,0.00004544383],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.3494039,0.002556319,0.319291,0.00179796,0.00103662,0.00007375388,0.0004510702,0.0003667813,0.3250225],"genre_scores_gemma":[0.9119792,0.001328744,0.03783638,0.0006366594,0.0006152983,0.0001010771,0.0003747285,0.0001422476,0.04698572],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007594835,"threshold_uncertainty_score":0.0254072,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03782610600975795,"score_gpt":0.3254781697518571,"score_spread":0.2876520637420992,"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."}}