The zeta polynomial of $P$ is the polynomial $z$ such that for every $i > 1$, $z(i)$ is the number of weakly increasing chains of $i-1$ vertices in $P$.
The zeta polynomial of the $n$ booleanLattice is $q^n$.
i1 : B = booleanLattice 3; |
i2 : z = zetaPolynomial B 3 o2 = q o2 : QQ[q] |
Thus, $z(2)$ is the number of vertices of $P$, and $z(3)$ is the number of total relations in $P$.
i3 : #B.GroundSet == sub(z, (ring z)_0 => 2) o3 = true |
i4 : #allRelations B == sub(z, (ring z)_0 => 3) o4 = true |
The object zetaPolynomial is a method function with options.