7 problems

Let $G_{\lambda}$ denote the stable Grothendieck polynomial indexed by a partition $\lambda$, and let $G_{(n)}$ and $G_{1^n}$ denote the elements indexed by the one-row and one-col…

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…

Stembridge equality analogue conjecture. There are analogues for $g_{\rho/\mu}$ and $G_{\rho/\mu}$ of the Stembridge equality

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…

Fix strict partitions $\mu\subseteq\lambda$. Let $G\hspace{-0.2mm}P^{(\beta)}_{\lambda/\mu}$ and $G\hspace{-0.2mm}Q^{(\beta)}_{\lambda/\mu}$ be the skew shifted stable Grothendieck…

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…