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# fultonGens -- compute the Fulton generators of an ASM ideal (for example, a Schubert determinantal ideal)

## Synopsis

• Usage:
fultonGens w
fultongens A
• Inputs:
• Optional inputs:
• CoefficientRing => a ring, default value QQ
• Variable => , default value z
• Outputs:

## Description

Given a partial alternating sign matrix or permutation in 1-line notation, returns the list of Fulton generators for the corresponding Schubert determinantal ideal or, more generally, ASM ideal.

 i1 : netList fultonGens({2,5,4,1,3}, CoefficientRing => ZZ/101) +---------------------+ o1 = |- z z + z z | | 1,2 2,1 1,1 2,2| +---------------------+ |- z z + z z | | 1,3 2,1 1,1 2,3| +---------------------+ |- z z + z z | | 1,3 2,2 1,2 2,3| +---------------------+ |- z z + z z | | 1,4 2,1 1,1 2,4| +---------------------+ |- z z + z z | | 1,4 2,2 1,2 2,4| +---------------------+ |- z z + z z | | 1,4 2,3 1,3 2,4| +---------------------+ |z | | 1,1 | +---------------------+ |z | | 2,1 | +---------------------+ |z | | 3,1 | +---------------------+ |- z z + z z | | 1,2 3,1 1,1 3,2| +---------------------+ |- z z + z z | | 2,2 3,1 2,1 3,2| +---------------------+ |- z z + z z | | 1,3 3,1 1,1 3,3| +---------------------+ |- z z + z z | | 2,3 3,1 2,1 3,3| +---------------------+ |- z z + z z | | 1,3 3,2 1,2 3,3| +---------------------+ |- z z + z z | | 2,3 3,2 2,2 3,3| +---------------------+ i2 : netList fultonGens(matrix{{0,1,0},{1,-1,1},{0,1,0}}, Variable => a) +---------------------+ o2 = |a | | 1,1 | +---------------------+ |- a a + a a | | 1,2 2,1 1,1 2,2| +---------------------+

## Ways to use fultonGens :

• fultonGens(List)
• fultonGens(Matrix)

## For the programmer

The object fultonGens is .