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Journal article
Boolean Witt vectors and an integral Edrei-Thoma theorem
Selecta mathematica (Basel, Switzerland), v 22(2), pp 595-629
01 Apr 2016
Abstract
Asubtraction-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.
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Details
- Title
- Boolean Witt vectors and an integral Edrei-Thoma theorem
- Creators
- James Borger - Australian Mathematical Sciences InstituteDarij Grinberg - Massachusetts Institute of Technology
- Publication Details
- Selecta mathematica (Basel, Switzerland), v 22(2), pp 595-629
- Publisher
- Springer Nature
- Number of pages
- 35
- Grant note
- DP120103541; FT110100728 / Australian Research Council
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000379167900005
- Scopus ID
- 2-s2.0-84946120481
- Other Identifier
- 991021862233804721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied