Combinatorics of K-theory via a K-theoretic Poirier-Reutenauer bialgebra

Rebecca Patrias; Pavlo Pylyavskyy

doi:10.1016/j.disc.2015.10.044

Combinatorics of K-theory via a K-theoretic Poirier-Reutenauer bialgebra

Rebecca Patrias, Pavlo Pylyavskyy

School of Mathematics

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17 Scopus citations

Abstract

We use the K-Knuth equivalence of Buch and Samuel (2015) to define a K-theoretic analogue of the Poirier-Reutenauer Hopf algebra. As an application, we rederive the K-theoretic Littlewood-Richardson rules of Thomas and Yong (2009, 2011) and of Buch and Samuel (2015).

Original language	English (US)
Pages (from-to)	1095-1115
Number of pages	21
Journal	Discrete Mathematics
Volume	339
Issue number	3
DOIs	https://doi.org/10.1016/j.disc.2015.10.044
State	Published - Mar 6 2016

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V.

Keywords

Bialgebra
K-theory
Symmetric functions

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10.1016/j.disc.2015.10.044

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abstract = "We use the K-Knuth equivalence of Buch and Samuel (2015) to define a K-theoretic analogue of the Poirier-Reutenauer Hopf algebra. As an application, we rederive the K-theoretic Littlewood-Richardson rules of Thomas and Yong (2009, 2011) and of Buch and Samuel (2015).",

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AU - Pylyavskyy, Pavlo

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N2 - We use the K-Knuth equivalence of Buch and Samuel (2015) to define a K-theoretic analogue of the Poirier-Reutenauer Hopf algebra. As an application, we rederive the K-theoretic Littlewood-Richardson rules of Thomas and Yong (2009, 2011) and of Buch and Samuel (2015).

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KW - Bialgebra

KW - K-theory

KW - Symmetric functions

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Combinatorics of K-theory via a K-theoretic Poirier-Reutenauer bialgebra

Abstract

Bibliographical note

Keywords

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