# Witt vectors, semirings, and total positivity

@article{Borger1970WittVS,
title={Witt vectors, semirings, and total positivity},
author={James M. Borger},
journal={arXiv: Combinatorics},
year={1970},
pages={273-329}
}
• J. Borger
• Published 11 October 2013
• Mathematics
• arXiv: Combinatorics
We extend the big and $p$-typical Witt vector functors from commutative rings to commutative semirings. In the case of the big Witt vectors, this is a repackaging of some standard facts about monomial and Schur positivity in the combinatorics of symmetric functions. In the $p$-typical case, it uses positivity with respect to an apparently new basis of the $p$-typical symmetric functions. We also give explicit descriptions of the big Witt vectors of the natural numbers and of the nonnegative…
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