Boolean Witt vectors and an integral Edrei–Thoma theorem

James Borger, Darij Grinberg

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)595-629
Number of pages35
JournalSelecta Mathematica, New Series
Volume22
Issue number2
DOIs
StatePublished - Apr 1 2016

Keywords

  • Boolean algebra
  • Schur positivity
  • Semiring
  • Symmetric function
  • Total positivity
  • Witt vector

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