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

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• 作者：Rebecca Patrias ; ^{patri080@umn.edu" class="auth_mail" title="E-mail the corresponding author} ; Pavlo Pylyavskyy ^{ppylyavs@umn.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Bialgebra ; KK-theory ; Symmetric functions
• 刊名：Discrete Mathematics
• 出版年：2016
• 出版时间：6 March 2016
• 年：2016
• 卷：339
• 期：3
• 页码：1095-1115
• 全文大小：481 K

文摘

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