Hierarchical Zonotopal Spaces
Hierarchical Zonotopal Spaces
Suppose is an matrix. Let denote the hyperplane generated by a submatrix , with and denote by the set of all . The normal to a hyperplane is denoted by ; let . Then the central and the external ideals are generated by and , respectively. The semi-external ideal is generated by , where . The kernel of the central and external ideals are zonotopal spaces, while the kernel of the semi-external ideal is a hierarchical zonotopal space. This Demonstration shows the Hilbert series and Gröbner basis of the semi-external ideal .
X=(,...)
x
1
x
n
s×n
H
Y
Y⊆X
rank(Y)=s-1
ℱ(X)
H
Y
H
ℓ
H
m(H)=#{x∈X|x∉H}
(H):H∈ℱ(X)
m(H)
ℓ
H
:H∈ℱ(X)
m(H)+1
ℓ
H
I
:H∈ℱ(X)
m(H)+ϵ(H)
ℓ
H
ϵ(H)∈{0,1}
I
I