Staircase equality for tableau and dual Grothendieck functions

Let $\rho_k=(k,k-1,\ldots,2,1)$ be the staircase partition, and let $gp_{\rho_k}({\bf y})$ and $g_{\rho_k}({\bf y})$ denote the tableau-defined and stable dual Grothendieck functions, respectively. Staircase equality. For the staircase partition $\rho_k$, one has

$$gp_{\rho_k}({\bf y})=g_{\rho_k}({\bf y}).$$

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