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tuttePolynomial -- computes the Tutte polynomial of a poset

Synopsis

Description

The Tutte polynomial of $P$ is a polynomial $f$ in two variables obtained by a summation over antichains.

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 
     ------------------------------------------------------------------------
         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 +
     ------------------------------------------------------------------------
       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  +
     ------------------------------------------------------------------------
       2      2
     3t z + 3t  + t + 1

o2 : QQ[t, z]

The Tutte polynomial evaluated 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

See also

Ways to use tuttePolynomial :

For the programmer

The object tuttePolynomial is a method function.