P-partition power sums
P-partition power sums
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P 分区幂和
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Stephanie van Willigenburg
中科院分区：
文献类型：
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作者：
F. Aliniaeifard;V. Wang;Stephanie van Willigenburg
我们发展了加权P-划分理论，它将P-划分理论从标号偏序集推广到加权标号偏序集。我们以自然的方式定义了相关的母函数，并计算了它们的乘积、余积等性质。作为应用，我们引入了拟对称函数的Hopf代数的组合幂和基和逆基，这两种基都是幂和对称函数的精化。这些基与Ballantine，Dauherty，Hicks，Mason和Niese提出的第一类和第二类拟对称幂和有许多共同的性质，并进一步扩展为具有非负整系数的拟对称函数的单项式基。我们通过P-分拆的组合学证明了乘积、余积和经典拟对称对合的公式，并给出了展开为单项基和基本基时系数的组合解释。
We develop the theory of weighted P-partitions, which generalises the theory of P-partitions from labelled posets to weighted labelled posets. We define the related generating functions in the natural way and compute their product, coproduct and other properties. As an application we introduce the basis of combinatorial power sums for the Hopf algebra of quasisymmetric functions and the reverse basis, both of which refine the power sum symmetric functions. These bases share many properties with the type 1 and type 2 quasisymmetric power sums introduced by Ballantine, Daugherty, Hicks, Mason and Niese, and moreover expand into the monomial basis of quasisymmetric functions with nonnegative integer coefficients. We prove formulas for products, coproducts and classical quasisymmetric involutions via the combinatorics of P-partitions, and give combinatorial interpretations for the coefficients when expanded into the monomial and fundamental bases.