{"id":"W2339763958","doi":"10.46298/dmtcs.2870","title":"Words and Noncommutative Invariants of the Hyperoctahedral Group","year":2010,"lang":"en","type":"article","venue":"Discrete Mathematics & Theoretical Computer Science","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"","keywords":"Mathematics; Combinatorics; Permutation group; Symmetric group; Morphism; Subalgebra; Permutation (music); Algebra over a field; Pure mathematics; Physics","routes":{"ca_aff":true,"ca_fund":false,"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":["sts"],"consensus_categories":[],"category_scores_codex":[0.001044375,0.0002184758,0.0003501177,0.00006362429,0.0003568832,0.0001403174,0.001266702,0.00008956176,0.00006886796],"category_scores_gemma":[0.0005721329,0.0001269988,0.00009942911,0.0004558474,0.004483018,0.0001819627,0.001085703,0.0004049802,0.000002098845],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001252693,"about_ca_system_score_gemma":0.00007525198,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003086388,"about_ca_topic_score_gemma":0.000003313797,"domain_scores_codex":[0.9981121,0.00006987817,0.00041835,0.0003435891,0.0007001782,0.0003558521],"domain_scores_gemma":[0.9979026,0.0007986866,0.0002090498,0.0008121133,0.000122823,0.0001547822],"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":[0.000005901445,0.00005440457,0.00006763088,0.00004224656,0.00001022228,7.824644e-7,0.003251767,7.784508e-7,0.001663252,0.9944135,0.000007351471,0.0004821424],"study_design_scores_gemma":[0.0002587759,0.0000776008,0.0002956597,0.00006476465,0.00003005437,0.00003293956,0.0001786801,0.02579516,0.002151812,0.9709443,0.00000491533,0.0001652707],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8572752,0.000005809932,0.1381371,0.000282705,0.0007722048,0.0002942597,0.000004342814,0.00003591489,0.003192492],"genre_scores_gemma":[0.8765485,9.025501e-7,0.1232687,0.00006961137,0.00008279552,0.000006941195,2.48042e-7,0.00001639915,0.000005920664],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02579438,"threshold_uncertainty_score":0.9982262,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01348468194081951,"score_gpt":0.2732945789962972,"score_spread":0.2598098970554776,"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."}}