9 problems

Let $F$ be a fence with $t$ segments. Let $I_H(F)$ be its ideal-statistic homomesic space and $I_T(F)$ its ideal-toggleability space. Full-range codimension conjecture. For every i…

Let $a$ be a positive integer, let $t$ be odd, and let $F=\breve{F}(a^t)$ be the uniform self-dual fence with $t$ segments. For $i\in\{1,\ldots,t-1\}$, let $s_i$ and $s_{t-i}$ be t…

Let $a$ be a positive integer, let $t$ be odd, and let $F=\breve{F}(a^t)$ be the uniform self-dual fence with $t$ segments. For each peak $p$ and valley $v$ of $F$, let $\chi_p$ an…

Let $a$ be a positive integer, let $t$ be odd, and let $F=\breve{F}(a^t)$ be the uniform self-dual fence with $t$ segments. Write $n=\#F$ for its number of elements, and let…

Let $F$ be a fence, and let $\hat{\chi}$ denote its order ideal cardinality statistic. Elizalde et al.'s homomesy conjecture. For certain fences, $\hat{\chi}$ is homomesic under ro…

Let $F(\beta)$ be a fence and let $L(\beta)$ be its lattice of lower order ideals. Suppose $k\ge 2$ and $\beta=(k-1,k,k,\ldots,k,k-1)$ has an odd number of parts. Under rowmotion o…

Let $F(\beta)$ be a fence and let $L(\beta)$ be its distributive lattice of lower order ideals. For a linear extension of $F(\beta)$, form the corresponding lexicographic chain dec…

Let $F(\beta)$ be a fence and let $L(\beta)$ be its distributive lattice of lower order ideals, with rank sequence governed by the alternatives in Theorem heavy. A saturated chain…

Let $F(\beta)$ be a fence with an even number of parts, and let $\overline{r}(\beta)$ denote the restricted rank sequence defined in the source. Oğuz–Ravichandran's conjecture. If…