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

Research output: Contribution to journal › Article › peer-review

16 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

Funding Information:
R.P. was supported by NSF grant DMS-1148634 . P.P. was supported by NSF grants DMS-1068169 , DMS-1148634 , DMS-1351590 , and Sloan Fellowship .

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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title = "Combinatorics of K-theory via a K-theoretic Poirier-Reutenauer bialgebra",

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).",

keywords = "Bialgebra, K-theory, Symmetric functions",

author = "Rebecca Patrias and Pavlo Pylyavskyy",

note = "Funding Information: R.P. was supported by NSF grant DMS-1148634 . P.P. was supported by NSF grants DMS-1068169 , DMS-1148634 , DMS-1351590 , and Sloan Fellowship . Publisher Copyright: {\textcopyright} 2015 Elsevier B.V.",

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AU - Patrias, Rebecca

AU - Pylyavskyy, Pavlo

N1 - Funding Information: R.P. was supported by NSF grant DMS-1148634 . P.P. was supported by NSF grants DMS-1068169 , DMS-1148634 , DMS-1351590 , and Sloan Fellowship . Publisher Copyright: © 2015 Elsevier B.V.

PY - 2016/3/6

Y1 - 2016/3/6

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).

AB - 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).

KW - Bialgebra

KW - K-theory

KW - Symmetric functions

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DO - 10.1016/j.disc.2015.10.044

M3 - Article

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VL - 339

SP - 1095

EP - 1115

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 3

ER -

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

Abstract

Bibliographical note

Keywords

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