Correlations in totally symmetric self‐complementary plane partitions

Totally symmetric self-complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry.We use the well-known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in 1/12 of a hexagon with free boundary to express them as perfect matchings of a family of non-bipartite planar graphs.Our main result is that the edges of the TSSCPPs form a Pfaffian point process, for which we give explicit formulas for the inverse Kasteleyn matrix.Preliminary analysis of these correlations are then used to give a precise conjecture for the limit shape of TSSCPPs in the scaling limit.