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摘要翻译：
受Buch与Grassmanian的K-理论有关的集值表的工作的推动，我们研究了六个组合Hopf代数。这些Hopf代数可以被认为是由对称函数、准对称函数、非交换对称函数和置换的Malvenuto-Reutenauer Hopf代数组成的Hopf代数的经典“平方”的K-理论类似物。此外，我们发展了集值P-分块理论，并研究了三个新的对称函数族：反平面分块的权母函数、弱集值表和值集表。
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英文标题：
《Combinatorial Hopf algebras and K-homology of Grassmanians》
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作者：
Thomas Lam, Pavlo Pylyavskyy
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be thought of as K-theoretic analogues of the by now classical ``square'' of Hopf algebras consisting of symmetric functions, quasisymmetric functions, noncommutative symmetric functions and the Malvenuto-Reutenauer Hopf algebra of permutations. In addition, we develop a theory of set-valued P-partitions and study three new families of symmetric functions which are weight generating functions of reverse plane partitions, weak set-valued tableaux and valued-set tableaux.
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PDF链接：
https://arxiv.org/pdf/0705.2189
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