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# augmentedRotheDiagram -- find the Rothe diagram of a partial alternating sign matrix together with the rank table determining the alternating sign matrix variety

## Synopsis

• Usage:
augmentedRotheDiagram w
augmentedRotheDiagram A
• Inputs:
• Outputs:

## Description

Given a permutation in 1-line notation or a partial alternating sign matrix returns the Rothe diagram (as a list) with the rank conditions at each diagram box.

 i1 : w = {2,5,4,1,3} o1 = {2, 5, 4, 1, 3} o1 : List i2 : augmentedRotheDiagram(w) o2 = {((1, 1), 0), ((2, 1), 0), ((2, 3), 1), ((2, 4), 1), ((3, 1), 0), ((3, ------------------------------------------------------------------------ 3), 1)} o2 : List i3 : A = matrix{{0,1,0},{1,-1,0},{0,0,0}} o3 = | 0 1 0 | | 1 -1 0 | | 0 0 0 | 3 3 o3 : Matrix ZZ <-- ZZ i4 : augmentedRotheDiagram(A) o4 = {((1, 1), 0), ((2, 2), 1), ((2, 3), 1), ((3, 2), 1), ((3, 3), 1)} o4 : List

## Ways to use augmentedRotheDiagram :

• augmentedRotheDiagram(List)
• augmentedRotheDiagram(Matrix)

## For the programmer

The object augmentedRotheDiagram is .