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On Dimensions of a Random Solid Diagram
Published online by Cambridge University Press: 11 October 2005
Abstract
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 in the limit $n\to\infty$.
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- 2005 Cambridge University Press
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