{"id":"W2068387692","doi":"10.1016/j.dam.2012.08.017","title":"Generating functions for inscribed polyominoes","year":2012,"lang":"en","type":"article","venue":"Discrete Applied Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal; Université du Québec à Trois-Rivières","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Polyomino; Mathematics; Combinatorics; Inscribed figure; Rectangle; Generating function; Diagonal; Regular polygon; Sublinear function; Discrete mathematics; Geometry","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":[0.001091127,0.00117915,0.0008580249,0.003432847,0.002119587,0.003484287,0.001701472,0.001333811,0.01211847],"category_scores_gemma":[0.003144466,0.0005365299,0.001099272,0.001773849,0.002732278,0.00268984,0.002115008,0.002798971,0.001302996],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001324809,"about_ca_system_score_gemma":0.0006334022,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007851876,"about_ca_topic_score_gemma":0.00106446,"domain_scores_codex":[0.9993668,0.0001477597,0.00002917952,0.00007636083,0.0002470858,0.0001327909],"domain_scores_gemma":[0.9984605,0.0007073527,0.0002461832,0.0001158976,0.0001757445,0.0002943007],"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":[0.00001949651,0.00002473835,0.0002249793,0.00002239673,0.000004371552,0.00006139996,0.0001516373,0.0009818922,0.0005022857,0.9928377,0.0008970904,0.004272033],"study_design_scores_gemma":[0.00001887306,0.00001383311,0.0003490038,0.00001840091,0.000007660175,0.0001016778,0.00007677094,0.008370105,0.000503112,0.9880617,0.002460324,0.0000185596],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6580424,0.0006379525,0.1827847,0.001341437,0.0005274275,0.0001353407,0.0006524947,0.0003057523,0.1555725],"genre_scores_gemma":[0.9060566,0.0008393156,0.03297668,0.0004305081,0.0006739635,0.0003553405,0.001130529,0.0003895122,0.05714755],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01211847,"threshold_uncertainty_score":0.04054028,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05300014329784335,"score_gpt":0.3208573589499337,"score_spread":0.2678572156520903,"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."}}