permSetOfASM -- finds the permutation set of an alternating sign matrix

Synopsis

Usage:

permSetOfASM A
Inputs:
- A, a matrix,
Outputs:
- a list,

Description

Given an alternating sign matrix $A$, this routine computes Perm$(A) = \{w \in S_n \mid A \leq w$, and $v \in S_n$ with $A \leq v \leq w$ implies $ v=w\}$ (where $\leq$ is in (strong) Bruhat order). This computation is performed by taking the antidiagonal initial ideal determined by $A$ and extracting the permutations indexing its components via schubertDecompose.

i1 : A = matrix{{0,1,0,0},{0,0,1,0},{1,-1,0,1},{0,1,0,0}}

o1 = | 0 1  0 0 |
     | 0 0  1 0 |
     | 1 -1 0 1 |
     | 0 1  0 0 |

              4       4
o1 : Matrix ZZ  <-- ZZ

i2 : permSetOfASM A

o2 = {{3, 4, 1, 2}, {2, 3, 4, 1}}

o2 : List

Ways to use permSetOfASM:

permSetOfASM(Matrix)

For the programmer

The object permSetOfASM is a method function.