Boolean Witt vectors and an integral Edrei–Thoma theorem
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چکیده
We give explicit descriptions of the Witt vectors of the Boolean semiring. This includes the big Witt vectors, the Schur Witt vectors, and the p-typical Witt vectors. We use this to determine the Schur Witt vectors of the natural numbers, which can be viewed as the classification of totally positive power series with integral coefficients, first observed by Davydov. We also determine the cardinality of the Witt vectors of the semiring quotient of the natural numbers by a single relation of the form n = n+ 1. It is countable for n = 0, 1, 2 but uncountable after that. 2010 Mathematics Subject Classification. Primary 13F35; Secondary 16Y60, 05E05, 05E10.
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تاریخ انتشار 2014