Simulating quantum computations with Tutte polynomials

Tutte Polynomials of Flower Graphs

Chain polynomials and Tutte polynomials

The recently introduced chain and sheaf polynomials of a graph are shown to be essentially equivalent to a weighted version of the Tutte polynomial. c © 2002 Elsevier Science B.V. All rights reserved.

Tutte Polynomials

Let ∆ be a finite sequence of n vectors from a vector space over any field. We consider the subspace of Sym(V) spanned by Q v∈S v, where S is a subsequence of ∆. A result of Orlik and Terao provides a doubly indexed direct sum of this space. The main theorem is that the resulting Hilbert series is the Tutte polynomial evaluation T (∆; 1 + x, y). Results of Ardila and Postnikov, Orlik and Terao,...

Tutte Polynomials and Link Polynomials

We show how the Tutte polynomial of a plane graph can be evaluated as the "homfly" polynomial of an associated oriented link. Then we discuss some consequences for the partition function of the Potts model, the Four Color Problem and the time complexity of the computation of the homfly polynomial.

Tutte polynomials for trees

We define two two-variable polynomials for rooted trees and one twovariable polynomial for unrooted trees, all of which are based on the coranknullity formulation of the Tutte polynomial of a graph or matroid. For the rooted polynomials, we show that the polynomial completely determines the rooted tree, i.e., rooted trees TI and T, are isomorphic if and only if f(T,) = f(T2). The corresponding ...