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Posets :: zetaPolynomial

zetaPolynomial -- computes the zeta polynomial of a poset

Synopsis

Description

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 qn.

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

See also

Ways to use zetaPolynomial :