isMinRankTable -- whether a matrix is the canonical rank table of some partial ASM

Synopsis

Usage:

isMinRankTable T
Inputs:
- T, a matrix,
Outputs:
- a Boolean value,

Description

Checks whether T is a the canonical rank table of some partial ASM. These are the rank tables that are constructed in Section 1 of [Wei] and from which the partial ASM can be determined using equation (21) of the same paper.

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

i1 : T = matrix {{0,1,1},{1,1,2},{1,2,3}}

o1 = | 0 1 1 |
     | 1 1 2 |
     | 1 2 3 |

              3       3
o1 : Matrix ZZ  <-- ZZ

i2 : isMinRankTable T

o2 = true

i3 : U = matrix {{1,1,1,1,1},{1,2,2,2,2},{1,2,2,2,3},{1,2,2,3,3}}

o3 = | 1 1 1 1 1 |
     | 1 2 2 2 2 |
     | 1 2 2 2 3 |
     | 1 2 2 3 3 |

              4       5
o3 : Matrix ZZ  <-- ZZ

i4 : isMinRankTable U

o4 = true

Ways to use isMinRankTable :

isMinRankTable(Matrix)

For the programmer

The object isMinRankTable is a method function.