For $3 \leq n \leq 6$, this function lists all antidiagonal initial ideals for ASMs of size $n$.
i1 : initialIdealsList 3
o1 = {ideal 0, monomialIdeal z , monomialIdeal(z z ), monomialIdeal
1,1 1,2 2,1
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(z , z z ), monomialIdeal (z , z ), monomialIdeal (z ,
1,1 1,2 2,1 1,1 1,2 1,1
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z ), monomialIdeal (z , z , z )}
2,1 1,1 1,2 2,1
o1 : List