2 citations
3 papers
math.CO2009
Refined enumerations of alternating sign matrices: monotone (d,m)-trapezoids with prescribed top and bottom row
Ilse Fischer
Monotone triangles are plane integer arrays of triangular shape with certain monotonicity conditions along rows and diagonals. Their significance is mainly due to the fact that the…
math.CO2009★ 2 cited
More refined enumerations of alternating sign matrices
Ilse Fischer, Dan Romik
We study a further refinement of the standard refined enumeration of alternating sign matrices (ASMs) according to their first two rows instead of just the first row, and more gene…
math.CO2009
The operator formula for monotone triangles - simplified proof and three generalizations
Ilse Fischer
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 formu…