Witt vectors, semirings, and total positivity

Autor:	Borger, James M.
Rok vydání:	2013
Předmět:	Mathematics - Combinatorics Mathematics - K-Theory and Homology Mathematics - Number Theory 13F35 13K05 16Y60 05E05 14P10
Druh dokumentu:	Working Paper
Popis:	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 reals, the second of which is a restatement of Edrei's theorem on totally positive power series. Finally we give some negative results on the relationship between truncated Witt vectors and $k$-Schur positivity, and we give ten open questions. Comment: The form as it will appear in the published volume. Some minor improvements to the text, some new references
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1310.3013 Zobrazit plný text záznamu View this record from Arxiv