4 problems

Let $\lambda$ and $\mu$ be partitions, and let $\widetilde G_\lambda(\mathbf x)$ denote the stable Grothendieck polynomial. Write $\lambda\vee\mu$ and $\lambda\wedge\mu$ for the jo…

Let $\mu$ be a strict partition. For strict partitions $\lambda\supseteq\mu$ with $\ell(\lambda)=\ell(\mu)$, let $\textsf{SD}_{\lambda/\mu}$ be the shifted skew diagram. A vertical…

Let $m,k\in\mathbb{Z}_{>0}$, let $\mu=(m^k)$, and let $\nu=(m+k-1,m+k-3,\dots,|m-k|+1)$. For partitions $\lambda$ and $\mu$ with $\mu\subseteq\lambda$, let…

A ribbon is a connected skew Young diagram containing no $2\times2$ block. For a ribbon $\alpha$, let $G_\alpha$ denote its stable Grothendieck polynomial, and let $\alpha^*$ denote…