Description
Let $\texttt{S}=K[x_1,\ldots,x_n]$, $\texttt{t}\geq 1$ and a
t-spread ideal
I. Then
I is called a
t-strongly stable ideal, if $[I_j]_t$ is a
t-strongly stable set for all $j$.
We recall that $[I_j]_t$ is the
t-spread part of the $j$-th graded component of
IMoreover, a subset $N\subset M_{n,d,t}$ is called a
t-strongly stable set if taking a
t-spread monomial $u\in N$, for all $j\in \mathrm{supp}(u)$ and all $i,\ 1\leq i\leq j$, such that $x_i(u/x_j)$ is a
t-spread monomial, then it follows that $x_i(u/x_j)\in N$.
Examples:
i1 : S=QQ[x_1..x_6]
o1 = S
o1 : PolynomialRing
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i2 : isTStronglyStableIdeal(ideal {x_1*x_3,x_1*x_5},2)
o2 = false
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i3 : isTStronglyStableIdeal(ideal {x_1*x_3,x_1*x_4,x_1*x_5,x_2*x_4,x_2*x_5},2)
o3 = true
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