The characteristic polynomial of a ranked poset is the generating function with variable $q$ such that the coefficient of $q^r$ is the sum overall vertices of rank $r$ of the Moebius function of $v$.
The characteristic polynomial of the chain of $n$ is $q^{n-1}(q-1)$.
i1 : n = 5; |
i2 : factor characteristicPolynomial chain n 3 o2 = (q) (q - 1) o2 : Expression of class Product |
And the characteristic polynomial of the booleanLattice of $n$ is $(q-1)^n$.
i3 : factor characteristicPolynomial booleanLattice n 5 o3 = (q - 1) o3 : Expression of class Product |
The object characteristicPolynomial is a method function with options.