3 problems

Fix a partition $\lambda$, and consider the ribbons whose row lengths are a permutation of the parts of $\lambda$, ordered by $G$ positivity: $A\leq B$ when…

Consider the partial order on $G$-equivalence classes of skew shapes defined by $A\leq B$ when $a_{A,\nu}\leq a_{B,\nu}$ for every partition $\nu$, equivalently when $G_B-G_A$ is…

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…