diagLexInitNW -- Diagonal initial ideal of an ASM ideal with respect to lex, starting from NW corner

Synopsis

Usage:

diagLexInitNW w

diagLexInitNW A
Inputs:
- w, a list, or A is a Matrix
Optional inputs:
- CoefficientRing => a ring, default value QQ
- Variable => a symbol, default value z
Outputs:
- a monomial ideal,

Description

Given a partial alternating sign matrix or a permutation in 1-line notation, returns the diagonal initial ideal of the corresponding ASM ideal or Schubert determinantal ideal with respect to lexicographic order, where the variables are ordered reading from left-to-right and top-to-bottom (starting in the northwest corner).

This function computes over the coefficient field of rational numbers unless an alternative is specified.

i1 : diagLexInitNW({1,3,2},CoefficientRing=>ZZ/3001)

o1 = monomialIdeal(z   z   )
                    1,1 2,2

                       ZZ
o1 : MonomialIdeal of ----[z   ..z   ]
                      3001  1,1   3,3

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

o2 = monomialIdeal (z   , z   , z   , z   , z   z   )
                     1,1   1,2   1,3   2,1   2,2 3,1

o2 : MonomialIdeal of QQ[z   ..z   ]
                          1,1   4,4

Ways to use diagLexInitNW :

diagLexInitNW(List)
diagLexInitNW(Matrix)

For the programmer

The object diagLexInitNW is a method function with options.