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• W209128445 abstract "For each positive integer n this paper considers a one-parameter family of complex-valued measures on the symmetric group S_n, depending on a complex parameter z. For parameter values z=p^f a prime power, this measure describes splitting probabilities for monic degree n polynomials over the finite field with p^f elements, conditioned on being square-free. It studies these measure in the special case z=1, and shows they have an interesting internal structure having a representation theoretic interpretation. These measures may provide data relevant to the hypothetical field with one element ${mathbb F_1}$. It additionally studies the case z=-1, which also has a representation-theoretic interpretation" @default.
• W209128445 created "2016-06-24" @default.
• W209128445 creator A5005612207 @default.
• W209128445 date "2016-04-01" @default.
• W209128445 modified "2023-09-27" @default.
• W209128445 title "A family of measures on symmetric groups and the field with one element" @default.
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• W209128445 doi "https://doi.org/10.1016/j.jnt.2015.09.003" @default.
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