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math.CO2005
A new proof of the refined alternating sign matrix theorem
Ilse Fischer
In the early 1980s, Mills, Robbins and Rumsey conjectured, and in 1996 Zeilberger proved a simple product formula for the number of alternating sign matrices with a 1…
math.CO2005
The number of monotone triangles with prescribed bottom row
Ilse Fischer
We show that the number of monotone triangles with prescribed bottom row (k_1,...,k_n) is given by a simple product formula which remarkably involves (shift) operators. Monotone tr…