11 problems

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…

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

Stanley's P-partitions conjecture. The function $K_P$ is symmetric if and only if $P$ is a Schur labeled skew shape poset.

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…

Minuscule doppelgänger set-valued $P$-partition conjecture. For every $\ell\geq 1$ and $e\geq 0$,

Minuscule doppelgänger down-degree generating-function conjecture. For every $\ell\geq 1$,

Let $(P,w)$ be a labeled poset, and let $K_{P,w}$ denote its $P$-partition generating function. A symmetric function is a formal power series invariant under permutations of its va…

Let $(P,\omega)$ be a labeled poset, let $\mathscr{L}(P,\omega)$ denote its linear extensions, and let $\operatorname{des}(\pi)$ denote the number of descents of a linear extension…

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…