{"id":"W2069932879","doi":"10.1090/s0002-9939-09-09929-8","title":"Splittings of monomial ideals","year":2009,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":99,"is_retracted":false,"has_abstract":true,"ca_institutions":"Lakehead University","funders":"Natural Sciences and Engineering Research Council of Canada; Banff International Research Station for Mathematical Innovation and Discovery; Oklahoma State University; Louisiana Board of Regents","keywords":"Monomial; Betti number; Monomial ideal; Bipartite graph; Mathematics; Cover (algebra); Ideal (ethics); Enhanced Data Rates for GSM Evolution; Combinatorics; Discrete mathematics; Pure mathematics; Graph; Polynomial ring; Computer science; Mathematical analysis; Artificial intelligence","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":[0.0007308836,0.0002771988,0.0003897161,0.001474029,0.001123055,0.001133111,0.0005393981,0.000232452,0.006116033],"category_scores_gemma":[0.002439144,0.0002609961,0.000538578,0.0006155983,0.00153374,0.002548378,0.001446753,0.001255597,0.0007710731],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006526769,"about_ca_system_score_gemma":0.0002891192,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004556394,"about_ca_topic_score_gemma":0.0008439397,"domain_scores_codex":[0.9994226,0.00005340123,0.00003405556,0.0001103169,0.0002231043,0.0001565037],"domain_scores_gemma":[0.9991565,0.0001917838,0.000106246,0.0001424296,0.000162517,0.0002406551],"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":[0.00008619921,0.00003829614,0.002310956,0.00004376311,0.00001150946,0.0002435567,0.0006961687,0.002143971,0.01365941,0.9644266,0.0007449561,0.01559471],"study_design_scores_gemma":[0.00002002857,0.00005695806,0.002210774,0.00003294788,0.00001790906,0.0004083605,0.0004699289,0.02019908,0.01878763,0.9500433,0.007726578,0.00002642591],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8121911,0.0004011896,0.1285846,0.0003076815,0.000173786,0.0000686271,0.0002176456,0.0002619553,0.05779348],"genre_scores_gemma":[0.9713453,0.0001644099,0.02064955,0.00005677635,0.0001186753,0.00002793294,0.0002307245,0.00007521279,0.007331335],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006116033,"threshold_uncertainty_score":0.02046019,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0245518883659366,"score_gpt":0.3133621273151606,"score_spread":0.288810238949224,"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."}}