10 problems

Let $w$ be a permutation, and let $\mathsf{PD}(w)$ be the set of pipe dreams for $w$ equipped with the chute-move partial order $\mathrel{\leq_{\mathrm{chute}}}$, where…

Let $I_w$ be the relevant matrix Schubert ideal, let $\prec'$ be the diagonal term order, and write $V(\operatorname{init}_{\prec'}(I_w))$ for the variety defined by its initial id…

Let $D'$ be a Go-diagram in a partition $\lambda$, and let $c\prec c'$ be a crossing and uncrossing pair in $D'$ with $D'(c)=\circ$. Let $D$ be obtained by replacing the stones at…

Let $D'$ be a Go-diagram in a partition $\lambda$, and let $c\prec c'$ be a crossing and uncrossing pair in $D'$ with $D'(c)=\circ$. Let $D$ be obtained by replacing the stones at…

Involution pipe-dream conjecture. If $y\in I_\infty^{(n)}$, then

For fixed $p,q\in(0,1)$, let $\boldsymbol{w}^{(q)}(n)\in S_n$ be the random permutation from the $q$-reduced pipe-dream model, and let $H^{(q)}$ be its height function. Let…

Let $p otin[0,1)$ and let $boldsymbol{w}^{(1)}=boldsymbol{w}^{(1)}(n)in Sn$ be the random permutation in the $q=1$ model. Write $operatorname{inv}(boldsymbol{w}^{(1)})$ for its num…

Let $\mathfrak X_w$ denote the relevant combinatorial object, let $\prec'$ be the chosen term order, and let $\mathcal T(\mathfrak X_w,\prec')$ be its tablet; let the support of a…

Schubert polynomials are polynomial representatives of Schubert classes, and their products have the form … Bumpless pipe dreams support left and right insertion algorithms that gi…

Let $X_w$ be a matrix Schubert variety associated to a permutation $w$, and let ${\tt init}(X_w)$ denote its Gröbner degeneration with respect to any diagonal term order. A bumples…