In 2007 Lam and Pylyavskyy found a combinatorial formula for the dual stable Grothendieck polynomials, which are the dual basis of the stable Grothendieck polynomials with respect to the Hall inner product. In 2016 Galashin, Grinberg, and Liu introduced refined dual stable Grothendieck polynomials by putting additional sequence of parameters in the combinatorial formula of Lam and Pylyavskyy. Grinberg conjectured a Jacobi–Trudi type formula for refined dual stable Grothendieck polynomials. In this paper this conjecture is proved by using bijections of Lam and Pylyavskyy.

中文翻译：

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精对偶稳定Grothendieck多项式的Jacobi–Trudi公式

在2007年，Lam和Pylyavskyy发现了双重稳定Grothendieck多项式的组合公式，这是关于Hall内部乘积的稳定Grothendieck多项式的对偶基础。2016年，Galashin，Grinberg和Liu引入了对偶稳定Grothendieck多项式，方法是将附加参数序列放入Lam和Pylyavskyy的组合公式中。格林伯格（Grinberg）猜想了雅可比-特鲁迪（雅可比-特鲁迪）型公式，用于精细的双稳态格洛腾迪克多项式。在本文中，通过使用Lam和Pylyavskyy的双射证明了这一猜想。