Bivariate Asymptotics for Striped Plane Partitions

Abstract

We give a new asymptotic formula for a refined enumeration of plane partitions. Specifically: color the parts πi,j of a plane partition π according to the equivalence class of i --- j (mod 2), and keep track of the sums of the 0-colored and 1-colored parts seperately. We find, for large plane partitions, that the difference between these two sums is asymptotically Gaussian (and we compute the mean and standard deviation of the distribution). Our approach is to modify a multivariate technique of Haselgrove and Temperley.