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liftingFunction -- compute values of a lifting function

Description

This function was added in version 1.2 of the package Jets.

Given a set $X$ and a natural number $s$, let $\mathcal{J}_s (X)$ be the set that contains the elements $x_0,\dots,x_s$ for every element $x\in X$. The depolarization map $\delta_s \colon \mathcal{J}_s (X)\to X$ is defined by $\delta_s (x_i) = x$ for every $x\in X$ and $i\in \{0,\dots,s\}$.

The lifting function $l_s (j,k)$ counts the number of subsets $V\subseteq \mathcal{J}_s (X)$ of cardinality $k$ such that $\delta_s (V) = U$, where $U\subseteq X$ is a fixed subset of cardinality $j$. Note that this number does not depend on $U$ but only on its cardinality. See F. Galetto, N. Iammarino, and T. Yu, Jets and principal components of monomial ideals, and very well-covered graphs for computing this function.

i1 : liftingFunction(1,2,3)

o1 = 4
i2 : liftingFunction(2,2,3)

o2 = 18
i3 : liftingFunction(1,3,2)

o3 = 0
i4 : liftingFunction(1,0,0)

o4 = 1

For uses of the lifting function, see Example 4.

Menu

Ways to use liftingFunction:

  • liftingFunction(ZZ,ZZ,ZZ)

For the programmer

The object liftingFunction is a method function.


The source of this document is in Jets.m2:1666:0.