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Posets :: characteristicPolynomial

characteristicPolynomial -- computes the characteristic polynomial of a ranked poset with a unique minimal element



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

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

o3 = (q - 1)

o3 : Expression of class Product

See also

Ways to use characteristicPolynomial :

For the programmer

The object characteristicPolynomial is a method function with options.