8 problems

Let $[a]\times[b]$ be the product of two chains, and let $\operatorname{NAR}$ denote noncommutative birational rowmotion on this poset, with labels taken in a noncommutative skew f…

Let $p$ be an integer with $p>1$, let $s\in\mathbb{N}$, and let $P$ be the subposet … of $[p]\times[p]$. Let $f\in\mathbb{K}^{\widehat{P}}$ be a $\mathbb{K}$-labeling such that…

Let $p$ be a positive integer, let $P=\operatorname{Tria}(p)$, where … and let $f\in\mathbb{K}^{\widehat{P}}$ be a $\mathbb{K}$-labeling such that $R^{2p}f\neq\operatorname{\bot}$.…

Let $p\geq2$ be an integer, and let $P=\nabla(p)$, where … Use the same notation as for the Delta-triangle: $f$ is a $[?]$-labeling of $\widehat{P}$, $R$ is birational rowmotion, a…

Let $p\geq2$ be an integer, and let $P=\Delta(p)$, where … Let $f\in\mathbb{K}^{\widehat{P}}$ be a $\mathbb{K}$-labeling such that $R^pf\neq\operatorname{\bot}$. Set $a=f(0)$ and…

Let $P$ be a rectangular poset, meaning a product of two chains, and let $\boldsymbol{K}$ be a field or, more generally, a noncommutative ring in the setting of the conjecture. Bir…

Let $\operatorname*{NEtri}(p)$ be the northeast triangular poset, let $s\in\mathbb{N}$, and define the subposet … Let $R_{\operatorname*{NEtri}\nolimits^{\prime}(p)}$ denote birati…

Let $\operatorname*{NEtri}(p)$ be the northeast triangular poset of the triangular poset construction, and let $R_{\operatorname*{NEtri}(p)}$ denote birational rowmotion on it. For…