Stanley's P-partitions conjecture on symmetric P-partition enumerators

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 preserving both the order relation and the set of strict edges. Stanley's $P$-partitions conjecture. Every finite labeled poset $(P,\omega)$ for which $\Gamma(P,\omega)$ is symmetric is isomorphic to a skew-diagram labeled poset. This conjecture remains open; work of Malvenuto and others has investigated its status.