  It was shown recently by the authors that, for any n, there is equality
between the distributions of certain triplets of statistics on nxn alternating
sign matrices (ASMs) and descending plane partitions (DPPs) with each part at
most n. The statistics for an ASM A are the number of generalized inversions in
A, the number of -1's in A and the number of 0's to the left of the 1 in the
first row of A, and the respective statistics for a DPP D are the number of
nonspecial parts in D, the number of special parts in D and the number of n's
in D. Here, the result is generalized to include a fourth statistic for each
type of object, where this is the number of 0's to the right of the 1 in the
last row of an ASM, and the number of (n-1)'s plus the number of rows of length
n-1 in a DPP. This generalization is proved using the known equality of the
three-statistic generating functions, together with relations which express
each four-statistic generating function in terms of its three-statistic
counterpart. These relations are obtained by applying the Desnanot-Jacobi
identity to determinantal expressions for the generating functions, where the
determinants arise from standard methods involving the six-vertex model with
domain-wall boundary conditions for ASMs, and nonintersecting lattice paths for
DPPs.
