论文标题
加权posets和Qsym的富集单基础（扩展摘要）
Weighted posets and the enriched monomial basis of QSym (extended abstract)
论文作者
论文摘要
Gessel的基本和Stembridge的峰值功能是（富集）$ P $ - 分区的生成功能。它们也是形式功率系列的两个显着亚代毛的碱基，分别是准对称函数环（QSYM）和峰的代数。 Hsiao引入了单一峰函数，这是由奇数整数组成索引的峰值代数的基础，它们与峰函数的关系模仿了QSym的单一和基本碱基之间的峰值。我们表明，将单峰的扩展到任何组合是QSym的新基础，并概括了HSIAO的结果，包括产品规则。为此，我们引入了POSET的加权变体，并研究了它们的生成功能。
Gessel's fundamental and Stembridge's peak functions are the generating functions for (enriched) $P$-partitions on labelled chains. They are also the bases of two significant subalgebras of formal power series, respectively the ring of quasisymmetric functions (QSym) and the algebra of peaks. Hsiao introduced the monomial peak functions, a basis of the algebra of peaks indexed by odd integer compositions whose relation to peak functions mimics the one between the monomial and fundamental bases of QSym. We show that the extension of monomial peaks to any composition is a new basis of QSym and generalise Hsiao's results including the product rule. To this end we introduce a weighted variant of posets and study their generating functions.
