{"id":"W4389118825","doi":"10.1016/j.jpaa.2023.107577","title":"The Scarf complex and betti numbers of powers of extremal ideals","year":2023,"lang":"en","type":"article","venue":"Journal of Pure and Applied Algebra","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada; Simons Foundation; National Science Foundation","keywords":"Betti number; Mathematics; Monomial ideal; Monomial; Square-free integer; Ideal (ethics); Simplicial complex; Combinatorics; Square (algebra); Discrete mathematics; Pure mathematics; Polynomial ring; Mathematical analysis; Geometry; Polynomial","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":[0.002398069,0.001191052,0.00193749,0.007346665,0.003292331,0.006856248,0.001987596,0.001773429,0.009436481],"category_scores_gemma":[0.01007154,0.001083006,0.000778102,0.002810061,0.006998525,0.009090615,0.002765279,0.003287936,0.0008116984],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001965428,"about_ca_system_score_gemma":0.0006294906,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00103883,"about_ca_topic_score_gemma":0.0009221868,"domain_scores_codex":[0.9988397,0.0002246236,0.000063885,0.0001856643,0.0004204177,0.0002657323],"domain_scores_gemma":[0.9955084,0.002169434,0.0007723444,0.0002921177,0.0003863448,0.0008712444],"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":[0.00005260255,0.00002171789,0.0003230719,0.00002547694,0.00000837844,0.00008578492,0.0002921051,0.0005446805,0.0004023662,0.9949765,0.0004737999,0.002793512],"study_design_scores_gemma":[0.00001169511,0.000007667406,0.0003134537,0.00001535558,0.00000536264,0.0001133222,0.0000800699,0.002554284,0.0002261675,0.9956844,0.0009750125,0.00001321149],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7624175,0.003825779,0.05986429,0.002680293,0.0007329527,0.00006292028,0.0002621087,0.0002010828,0.1699531],"genre_scores_gemma":[0.9837467,0.0008284589,0.004397133,0.0001368823,0.0006464781,0.00003721772,0.0001266705,0.00006005155,0.01002039],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009436481,"threshold_uncertainty_score":0.03156817,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04519392099104821,"score_gpt":0.3182335519982828,"score_spread":0.2730396310072347,"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."}}