essentialSet -- compute the essential set in the Rothe Diagram for a partial alternating sign matrix or a permutation.

Synopsis

Usage:

essentialSet w

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

Description

Given an alternating sign matrix or a permutation in 1-line notation, outputs Fulton's essential set, i.e., the maximally southeast elements of the Rothe diagram of that alternating sign matrix or permutation.

i1 : essentialSet({1,3,2})

o1 = {(2, 2)}

o1 : List

i2 : essentialSet(matrix{{0,0,0,1},{0,1,0,0},{1,-1,1,0},{0,1,0,0}})

o2 = {(1, 3), (2, 1), (3, 2)}

o2 : List

Ways to use essentialSet :

essentialSet(List)
essentialSet(Matrix)

For the programmer

The object essentialSet is a method function.