Galois groups of multivariate Tutte polynomials

Details Galois groups of multivariate Tutte polynomials Galois groups of multivariate Tutte polynomials

2010-06-19

arxiv.org/abs/1006.3869v4

Mathematics

Combinatorics

8 pages, final version, to appear in J. Alg. Comb. Substantial revisions, including the addition of two alternative proofs of

Scientific paper

The multivariate Tutte polynomial $\hat Z_M$ of a matroid $M$ is a generalization of the standard two-variable version, obtained by assigning a separate variable $v_e$ to each element $e$ of the ground set $E$. It encodes the full structure of $M$. Let $\bv = \{v_e\}_{e\in E}$, let $K$ be an arbitrary field, and suppose $M$ is connected. We show that $\hat Z_M$ is irreducible over $K(\bv)$, and give three self-contained proofs that the Galois group of $\hat Z_M$ over $K(\bv)$ is the symmetric group of degree $n$, where $n$ is the rank of $M$. An immediate consequence of this result is that the Galois group of the multivariate Tutte polynomial of any matroid is a direct product of symmetric groups. Finally, we conjecture a similar result for the standard Tutte polynomial of a connected matroid.

Affiliated with

Also associated with

No associations

Rating

Galois groups of multivariate Tutte polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Galois groups of multivariate Tutte polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Galois groups of multivariate Tutte polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-431603