Some inequalities for the Tutte polynomial
Combinatorics
2010-04-16 v1
Abstract
We prove that the Tutte polynomial of a coloopless paving matroid is convex along the portions of the line segments x+y=p lying in the positive quadrant. Every coloopless paving matroids is in the class of matroids which contain two disjoint bases or whose ground set is the union of two bases of M*. For this latter class we give a proof that T_M(a,a) <= max {T_M(2a,0), T_M(0,2a)} for a >= 2. We conjecture that T_M(1,1) <= max {T_M(2,0), T_M(0,2)} for the same class of matroids. We also prove this conjecture for some families of graphs and matroids.
Cite
@article{arxiv.1004.2639,
title = {Some inequalities for the Tutte polynomial},
author = {L. E. Chavez-Lomelí and C. Merino and S. D. Noble and M. Ramírez-Ibañez},
journal= {arXiv preprint arXiv:1004.2639},
year = {2010}
}
Comments
17 pages