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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 $H^{\\bullet}(P_n, \\mathbb{Q})$. 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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 $H^{\\bullet}(P_n, \\mathbb{Q})$. 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