The Tutte polynomial of $P$ is the polynomial $f$ such that
i1 : B = booleanLattice 3; |
i2 : f = tuttePolynomial B
8 7 8 6 8 5 8 4 8 3 7 4 8 2 7 3 6 4
o2 = t z + 7t z + 21t z + 35t z + 35t z + t z + 21t z + 4t z + 3t z
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8 7 2 6 3 8 7 6 2 5 3 7 6
+ 7t z + 6t z + 12t z + t + 4t z + 18t z + 3t z + t + 12t z +
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5 2 4 3 6 5 4 2 5 4 4 3 3
9t z + 3t z + 3t + 9t z + 9t z + 3t + 10t z + 4t + 3t z + 3t +
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2 2
3t z + 3t + t + 1
o2 : QQ[t, z]
|
The Tutte polynomial evaluates at $t = 1$ and $z = 1$ is always the number of subsets of the groundset of $P$.
i3 : R = ring f; |
i4 : sub(f, {R_0 => 1, R_1 => 1})
o4 = 256
o4 : QQ
|
The object tuttePolynomial is a method function.