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# cohenMacaulayASMsList -- lists all Cohen-Macaulay ASMs of a fixed size which are not permutation matrices

## Synopsis

• Usage:
cohenMacaulayASMsList n
• Inputs:

## Description

For $1 \leq n \leq 6$, this function lists all $n\times n$ alternating sign matrices $A$ which are not permutation matrices such that the corresponding ASM variety is Cohen-Macaulay. By a theorem of Fulton [Ful92], permutation matrices always have Cohen-Macaulay Schubert determinantal ideals.

 i1 : cohenMacaulayASMsList(4) o1 = {| 0 1 0 0 |, | 1 0 0 0 |, | 0 1 0 0 |, | 0 0 1 0 |, | 0 1 0 0 |, | 1 -1 1 0 | | 0 0 1 0 | | 1 -1 1 0 | | 1 0 0 0 | | 0 0 1 0 | | 0 1 0 0 | | 0 1 -1 1 | | 0 1 -1 1 | | 0 1 -1 1 | | 1 0 -1 1 | | 0 0 0 1 | | 0 0 1 0 | | 0 0 1 0 | | 0 0 1 0 | | 0 0 1 0 | ------------------------------------------------------------------------ | 0 0 1 0 |, | 0 1 0 0 |, | 0 0 1 0 |, | 0 1 0 0 |, | 0 0 1 0 |, | | 0 1 0 0 | | 1 -1 0 1 | | 0 1 -1 1 | | 1 -1 1 0 | | 0 1 0 0 | | | 1 0 -1 1 | | 0 1 0 0 | | 1 0 0 0 | | 0 0 0 1 | | 1 -1 0 1 | | | 0 0 1 0 | | 0 0 1 0 | | 0 0 1 0 | | 0 1 0 0 | | 0 1 0 0 | | ------------------------------------------------------------------------ 0 1 0 0 |, | 0 0 1 0 |, | 0 1 0 0 |, | 0 0 0 1 |, | 0 0 1 0 |} 1 -1 0 1 | | 1 0 -1 1 | | 0 0 0 1 | | 0 1 0 0 | | 0 1 -1 1 | 0 0 1 0 | | 0 0 1 0 | | 1 -1 1 0 | | 1 -1 1 0 | | 0 0 1 0 | 0 1 0 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 1 0 0 | | 1 0 0 0 | o1 : List

## Ways to use cohenMacaulayASMsList :

• cohenMacaulayASMsList(ZZ)

## For the programmer

The object cohenMacaulayASMsList is .