We introduce an enriched analogue of Lam and Pylyavskyy’s theory of set-valued P-partitions. An an application, we construct a K-theoretic version of Stembridge’s Hopf algebra of peak quasisymmetric functions. We show that the symmetric part of this algebra is generated by Ikeda and Naruse’s shifted stable Grothendieck polynomials. We give the first proof that the natural skew analogues of these power series are also symmetric. A central tool in our constructions is a “K-theoretic” Hopf algebra of labeled posets, which may be of independent interest. Our results also lead to some new explicit formulas for the involution \(\omega \) on the ring of symmetric functions.

我们介绍了Lam和Pylyavskyy的集值P分区理论的丰富类比。在一个应用程序中，我们构造了峰值准对称函数的Stembridge's Hopf代数的K理论版本。我们证明了该代数的对称部分是由池田和成濑的移位稳定格洛腾迪克多项式生成的。我们给出第一个证明，即这些幂级数的自然偏斜类似物也是对称的。在我们的构造中，一个中心工具是带有标记的位姿的“ K理论”霍夫夫代数，这可能是与您无关的。我们的结果还为对称函数环上的对合\（\ omega \）产生了一些新的显式公式。