augmentedRotheDiagram -- find the Rothe diagram and rank table for a partial ASM or permutation

Usage:

augmentedRotheDiagram w

augmentedRotheDiagram A
Inputs:
- w, a list, or A is a Matrix
Outputs:
- a list,

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 a method function.

The source of this document is in MatrixSchubert/MatrixSchubertConstructionsDOC.m2:723:0.