Boolean Witt vectors and an integral Edrei–Thoma theorem
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Author(s)
Borger, James
Grinberg, Darij
Date Issued
November 2015
Journal
Selecta Mathematica
Publisher
Springer International Publishing
Citation
Borger, James, and Darij Grinberg. “Boolean Witt Vectors and an Integral Edrei–Thoma Theorem.” Selecta Mathematica 22, no. 2 (November 4, 2015): 595–629.
Version
Author's final manuscript
Abstract
A subtraction-free definition of the big Witt vector construction was recently given by the first author. This allows one to define the big Witt vectors of any semiring. Here we give an explicit combinatorial description of the big Witt vectors of the Boolean semiring. We do the same for two variants of the big Witt vector construction: the Schur Witt vectors and the p-typical Witt vectors. We use this to give an explicit description of the Schur Witt vectors of the natural numbers, which can be viewed as the classification of totally positive power series with integral coefficients, first obtained by Davydov. We also determine the cardinalities of some Witt vector algebras with entries in various concrete arithmetic semirings.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00029-015-0198-6
