{"id":"W2581995822","doi":"10.1016/j.disc.2018.01.017","title":"Characterizing the number of coloured <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"mml1\" display=\"inline\" overflow=\"scroll\" altimg=\"si1.gif\"><mml:mi>m</mml:mi></mml:math>-ary partitions modulo <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"mml2\" display=\"inline\" overflow=\"scroll\" altimg=\"si1.gif\"><mml:mi>m</mml:mi></mml:math>, with and without gaps","year":2018,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Modulo; Mathematics; Combinatorics; Discrete mathematics; Characterization (materials science); Arithmetic","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":[0.002942946,0.0007717325,0.001036189,0.002139333,0.002476039,0.006275175,0.002258323,0.001694006,0.0156377],"category_scores_gemma":[0.02567116,0.0005981401,0.0008109856,0.001463907,0.004795891,0.008263379,0.00354919,0.002304573,0.003252263],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001977136,"about_ca_system_score_gemma":0.001468018,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001019154,"about_ca_topic_score_gemma":0.00119599,"domain_scores_codex":[0.997029,0.0004679168,0.0002044271,0.0008211576,0.000780666,0.0006968908],"domain_scores_gemma":[0.986661,0.007251412,0.001328078,0.001887208,0.001678617,0.001193667],"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":[0.000737517,0.0001031545,0.004868172,0.0003008314,0.00002748997,0.0002937635,0.001291061,0.007560569,0.004720316,0.9428352,0.01158958,0.02567231],"study_design_scores_gemma":[0.00005603682,0.000105021,0.002387134,0.0001542581,0.00003633739,0.0006251008,0.0007338518,0.02774714,0.007871962,0.9443982,0.01582559,0.00005939154],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5856143,0.001664515,0.2790013,0.002606769,0.0006684408,0.0001775896,0.003277447,0.001455221,0.1255345],"genre_scores_gemma":[0.9386815,0.0005130033,0.04134538,0.0002644729,0.000303302,0.0001581735,0.001748113,0.0007443813,0.01624164],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0156377,"threshold_uncertainty_score":0.05231333,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02256427158167709,"score_gpt":0.2748623648028583,"score_spread":0.2522980932211812,"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."}}