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Posets :: characteristicPolynomial

characteristicPolynomial -- computes the characteristic polynomial of a ranked poset

Synopsis

Description

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

See also

Ways to use characteristicPolynomial :