4 problems

Let $P$ be a circular fence poset of size $n$, let $S_n(P)$ denote the relevant set of permutations, and let $\widehat{bl}_P(\sigma)$ be the block statistic introduced for circular…

Let $k$ and $n$ be fixed positive integers with $k\mid n$, let $\alpha$ be a composition of $n$ with $k$ parts, and let $r(\alpha)$ denote its pointwise rank sequence. Balanced-com…

Let $\alpha$ be a composition of $n$, let $F(\alpha)$ be the associated fence poset, and write $r(\alpha)$ for its rank sequence, with inequalities interpreted pointwise. Extremal…

Constant-parameter homomesy conjecture.