The operator formula for monotone triangles - simplified proof and three generalizations

Details The operator formula for monotone triangles - simplified proof and three generalizations The operator formula for monotone triangles - simplified proof and three generalizations

2009-03-26

arxiv.org/abs/0903.4628v1

Mathematics

Combinatorics

Scientific paper

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.

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