Description
the function
countTStronglyStableMon(u,t) gives the cardinality of $B_t\{u\}$, the
tstrongly stable set generated by
u, that is, the number of all the
tspread monomials belonging to the smallest
tstrongly 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
tstrongly stable set if taking a
tspread 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
tspread monomial, then it follows that $x_i(u/x_j)\in N$.
Examples:
i1 : S=QQ[x_1..x_9]
o1 = S
o1 : PolynomialRing

i2 : countTStronglyStableMon(x_2*x_5*x_8,2)
o2 = 14

i3 : countTStronglyStableMon(x_2*x_5*x_8,3)
o3 = 4
