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# rankTableToASM -- to find the a partial ASM associated to a given rank table

## Synopsis

• Usage:
rankTableToASM T
• Inputs:
• T, ,
• Outputs:
• ,

## Description

Given a matrix that is a valid minimal rank table, returns the unique partial ASM of the same size associated to it. This algorithm follows

• [Wei, Equation (21)]: Weigandt, Prism tableaux for alternating sign matrix varieties (see arXiv:1708.07236).

 i1 : T = matrix {{0,0,1,1},{0,1,1,2},{1,2,2,3},{1,2,3,4}} o1 = | 0 0 1 1 | | 0 1 1 2 | | 1 2 2 3 | | 1 2 3 4 | 4 4 o1 : Matrix ZZ <-- ZZ i2 : rankTableToASM T o2 = | 0 0 1 0 | | 0 1 -1 1 | | 1 0 0 0 | | 0 0 1 0 | 4 4 o2 : Matrix ZZ <-- ZZ i3 : U = matrix {{0,0,1,1,1},{1,1,1,2,2},{1,2,2,3,3},{1,2,3,4,4},{1,2,3,4,5}} o3 = | 0 0 1 1 1 | | 1 1 1 2 2 | | 1 2 2 3 3 | | 1 2 3 4 4 | | 1 2 3 4 5 | 5 5 o3 : Matrix ZZ <-- ZZ i4 : rankTableToASM U o4 = | 0 0 1 0 0 | | 1 0 -1 1 0 | | 0 1 0 0 0 | | 0 0 1 0 0 | | 0 0 0 0 1 | 5 5 o4 : Matrix ZZ <-- ZZ

## Ways to use rankTableToASM :

• rankTableToASM(Matrix)

## For the programmer

The object rankTableToASM is .