STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Negative association in uniform forests and connected graphs
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part II
Negative correlation in graphs and matroids
Combinatorics, Probability and Computing
Inapproximability of the Tutte polynomial
Information and Computation
Combinatorics, Probability and Computing
On some Tutte polynomial sequences in the square lattice
Journal of Combinatorial Theory Series B
| Hi-index | 0.00 |
We introduce and prove a family of inequalities satisfied by the Whitney rank generating function of a matroid in the positive quadrant of ℝ2. These can be interpreted as correlation inequalities at those points where the polynomial is known to count the number of independent sets, bases or spanning sets of the matroid. Our proofs also introduce an idea of rank dominating bijections in matroids, which are then used to obtain some simple extensions of the submodular property of matroid ranks.