{"paper":{"title":"Polynomial splitting measures and cohomology of the pure braid group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO","math.NT"],"primary_cat":"math.RT","authors_text":"Jeffrey C. Lagarias, Trevor Hyde","submitted_at":"2016-04-18T21:47:33Z","abstract_excerpt":"We study for each $n$ a one-parameter family of complex-valued measures on the symmetric group $S_n$, which interpolate the probability of a monic, degree $n$, square-free polynomial in $\\mathbb{F}_q[x]$ having a given factorization type. For a fixed factorization type, indexed by a partition $\\lambda$ of $n$, the measure is known to be a Laurent polynomial. We express the coefficients of this polynomial in terms of characters associated to $S_n$-subrepresentations of the cohomology of the pure braid group $H^{\\bullet}(P_n, \\mathbb{Q})$. We deduce that the splitting measures for all parameter "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05359","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}