7 problems

Stanley's symmetry characterization conjecture. If $K_P$ is symmetric, then $P\in\sfSP_n$.

Minuscule P-partition cyclic sieving conjecture. For every $\ell\geq 1$, the triple

Minuscule P-partition rowmotion orbit conjecture. For every $\ell\geq 1$, there is a bijection $\varphi$ between the $\mathrm{row}$-orbits of $\mathrm{PP}^{\ell}(P)$ and those of…

Let $(P,\omega)$ be a finite labeled poset, and let $\Gamma(P,\omega)$ be its $P$-partition enumerator, a quasisymmetric function. An isomorphism of labeled posets is a bijection p…

A labelled poset $P$ has a $P$-partition enumerator $F_P({\mathbf{x}})$, which is always quasisymmetric; a labelling is column-strict when it has the column-strict property used fo…

Let $P$ be a connected $d$-complete poset with maximum element $v_0$, rank function $r:P\to\mathbb{N}$, top tree $T$, and $d$-complete coloring $c:P\to T$. Let…

Let $(P,\omega)$ and $(Q,\tau)$ be naturally labeled posets, meaning that the labeling is compatible with the poset order. Write $(P,\omega)\sim(Q,\tau)$ when their $P$-partition g…