Ilse Fischer
Published 2009-03-26Version 1
We provide a simplified proof of our operator formula for the number of monotone triangles with prescribed bottom row, which enables us to deduce three generalizations of the formula. One of the generalizations concerns a certain weighted enumeration of monotone triangles which specializes to the weighted enumeration of alternating sign matrices with respect to the number of -1s in the matrix when prescribing $(1,2,...,n)$ as the bottom row of the monotone triangle.
More refined enumerations of alternating sign matrices
An Izergin-Korepin-type identity for the 8VSOS model, with applications to alternating sign matrices
Factorization theorems for classical group characters, with applications to alternating sign matrices and plane partitions
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