Boolean Witt vectors and an integral Edrei-Thoma theorem
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.
The paper's page at arxiv.org
The paper's page at Selecta Mathematica.
2013-Jun-20: Preprint online
2013-Oct-18: Revised version online
2013-Nov-18: Revised version online and uploaded to the archive
2014-Aug-22: Revised version online
2015-Nov-04: Online at Selecta
2015-Dec-11: Final version online