The characteristic polynomial of a ranked poset is the generating function with variable q such that the coefficient of qr is the sum overall vertices of rank r of the Moebius function of v.
The characteristic polynomial of the chain of n is qn-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 |