{"id":"W2951058515","doi":"10.48550/arxiv.math/0609339","title":"On distinguishing trees by their chromatic symmetric functions","year":2006,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Combinatorics; Symmetric function; Mathematics; Monomial; Chromatic scale; Elementary symmetric polynomial; Power sum symmetric polynomial; Function (biology); Complete homogeneous symmetric polynomial; Invariant (physics); Ring of symmetric functions; Symmetric polynomial; Stanley symmetric function; Isomorphism (crystallography); Chromatic polynomial; Discrete mathematics; Polynomial; Orthogonal polynomials; Mathematical analysis; Matrix polynomial","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002363511,0.0006191993,0.0007576023,0.0004226458,0.0002995092,0.0001095443,0.000901742,0.0004273455,0.00005702933],"category_scores_gemma":[0.001446895,0.0006412242,0.0003564919,0.0008967221,0.000121248,0.00014206,0.000710847,0.0009492972,0.00008314421],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006641524,"about_ca_system_score_gemma":0.00009004112,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007296004,"about_ca_topic_score_gemma":0.00003975138,"domain_scores_codex":[0.9977853,0.0001636258,0.0004629848,0.0009158205,0.0001879697,0.0004842966],"domain_scores_gemma":[0.9953984,0.002133465,0.0007165494,0.00142195,0.0001721094,0.0001575085],"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":[0.00003367061,0.0009055846,0.0002259795,0.0005897825,0.0002382754,0.0001251206,0.0001868565,0.01574071,0.00003308734,0.9635172,0.01810036,0.0003033508],"study_design_scores_gemma":[0.0005937223,0.00008857728,0.00003921652,0.0004991991,0.0002727277,0.000003784799,0.0001432727,0.0255192,0.0001145833,0.9717721,0.0003097205,0.0006438583],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7339562,0.00007293506,0.2301692,0.00004270894,0.001629514,0.0008473903,0.0002655823,0.0008483639,0.03216819],"genre_scores_gemma":[0.9926229,0.00001796769,0.001451673,0.00001759382,0.0001917795,0.000005191834,0.00009271998,0.0001103806,0.005489808],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2586668,"threshold_uncertainty_score":0.9996039,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08479929283050675,"score_gpt":0.2131891379140501,"score_spread":0.1283898450835433,"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."}}