{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004716219,0.0001547511,0.0005321733,0.00001876964,0.00009534707,0.00001656976,0.0005806707,0.00003711584,0.00003492973],"category_scores_gemma":[0.000592085,0.0001036837,0.0004379293,0.0004925837,0.0005647715,0.00008339507,0.0001424418,0.0001674131,0.000004940563],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003496305,"about_ca_system_score_gemma":0.00002271901,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005437996,"about_ca_topic_score_gemma":7.206056e-8,"domain_scores_codex":[0.9987172,0.00000804222,0.0005666757,0.0001765454,0.0003141944,0.0002172681],"domain_scores_gemma":[0.9981178,0.0004380301,0.0009201342,0.0002212025,0.0002407,0.0000621438],"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":[0.00001643678,0.0003403688,0.0006499681,0.0002163005,0.00007327856,1.499323e-8,0.00310014,2.457116e-7,0.05481018,0.9303073,0.007814705,0.002671036],"study_design_scores_gemma":[0.0001623804,0.0001161086,0.004712156,0.00008391374,0.00008373721,0.000003145215,0.001603343,0.0002893991,0.03263476,0.9600801,0.0001107469,0.0001202417],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9842269,0.00001180767,0.001209265,0.002484516,0.000007061756,0.0003494952,0.000006072423,0.00004955012,0.01165529],"genre_scores_gemma":[0.9215409,0.00000981682,0.07796822,0.0002656697,0.00003595557,0.00001656288,1.754997e-7,0.00001505968,0.0001476007],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07675895,"threshold_uncertainty_score":0.4228098,"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."}}