Macaulay2 » Documentation
Packages » TSpreadIdeals > countTStronglyStableMon
next | previous | forward | backward | up | index | toc

countTStronglyStableMon -- give the cardinality of the t-strongly stable set generated by a given monomial



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 u
This 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 $x_i(u/x_j)\in N$.


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

See also

Ways to use countTStronglyStableMon :

For the programmer

The object countTStronglyStableMon is a method function.