The University of Michigan Combinatorics Seminar
A solid diagram of volume n is a packing of n unit cubes into
a corner so that the heights of vertical stacks of cubes do not increase in
either of two horizontal directions away from the corner. An asymptotic
distribution of the dimensions---heights, depths, and widths---of the diagram
chosen uniformly at random among all such diagrams is studied. For each k,
the planar base of k tallest stacks is shown to be Plancherel distributed.