Description
the function
countTStronglyStableMon(u,t) gives the cardinality of $B_t\{u\}$, the
t-strongly stable set generated by
u, that is, the number of all the
t-spread monomials belonging to the smallest
t-strongly stable set containing
uThis method is not constructive. It uses a theoretical result to obtain the cardinality as the sum of suitable binomial coefficients. The procedure only concerns $\textrm{supp}(\texttt{u}),$ that is, the set $\{i_1,i_2,\ldots, i_d\}$, when $u=x_{i_1}x_{i_2}\cdots x_{i_d}$ is a $t$-spread monomial.
Moreover, 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_9]
o1 = S
o1 : PolynomialRing
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i2 : countTStronglyStableMon(x_2*x_5*x_8,2)
o2 = 14
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i3 : countTStronglyStableMon(x_2*x_5*x_8,3)
o3 = 4
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