A Tutte polynomial inequality for lattice path matroids

@article{Knauer2015ATP,
  title={A Tutte polynomial inequality for lattice path matroids},
  author={Kolja B. Knauer and Leonardo Mart{\'i}nez-Sandoval and Jorge L. Ram{\'i}rez Alfons{\'i}n},
  journal={ArXiv},
  year={2015},
  volume={abs/1510.00600}
}

Figures from this paper

Lattice path matroids and quotients

We characterize the quotients among lattice path matroids (LPMs) in terms of their diagrams. This characterization allows us to show that ordering LPMs by quotients yields a graded poset, whose rank

On Lattice Path Matroid Polytopes: Integer Points and Ehrhart Polynomial

It is proved that lattice path matroidpolytopes are affinely equivalent to a family of distributive polytopes and two new infinite families of matroids are obtained verifying a conjecture of De Loera et al.

On Lattice Path Matroid Polytopes: Integer Points and Ehrhart Polynomial

In this paper we investigate the number of integer points lying in dilations of lattice path matroid polytopes. We give a characterization of such points as polygonal paths in the diagram of the

Explorations in combinatorial geometry : Distinct circumradii, geometric Hall-type theorems, fractional Turán-type theorems, lattice path matroids and Kneser transversals

Combinatorial geometry is a broad and beautiful branch of mathematics. This PhD Thesis consists of the study of five different topics in this area. Even though the problems and the tools used to

The Merino--Welsh conjecture for split matroids

. In 1999 Merino and Welsh conjectured that evaluations of the Tutte polynomial of a graph satisfy an inequality. In this short article we show that the conjecture generalized to matroids holds for

Asymptotic behavior of acyclic and cyclic orientations of directed lattice graphs

Study of Exponential Growth Constants of Directed Heteropolygonal Archimedean Lattices

The inferred upper and lower bounds on the growth constants are quite close to each other, which enables us to infer rather accurate estimates for the actual exponential growth constants, and provide further support for the Merino–Welsh and Conde–Merino conjectures.

On the Ehrhart Polynomial of Minimal Matroids

  • L. Ferroni
  • Mathematics
    Discrete & Computational Geometry
  • 2021
We provide a formula for the Ehrhart polynomial of the connected matroid of size n and rank k with the least number of bases, also known as a minimal matroid. We prove that their polytopes are

References

SHOWING 1-10 OF 25 REFERENCES

Computing the Tutte polynomial of lattice path matroids using determinantal circuits

Lattice Path Matroid Polytopes

Fix two lattice paths P and Q from (0,0) to (m,r) that use East and North steps with P never going above Q. Bonin et al. in [1] show that the lattice paths that go from (0,0) to (m,r) and remain

An inequality for Tutte polynomials

It is shown that the Tutte polynomial of G satisfies the inequality TG(b, 0)TG(0, b) ≥ TG(a, a)2.

Lattice Path Matroids: Negative Correlation and Fast Mixing

Catalan numbers arise in many enumerative contexts as the counting sequence of combinatorial structures. In this work, we consider natural Markov chains on some of the realizations of the Catalan

Toric ideals of lattice path matroids and polymatroids

Multi-Path Matroids

The minor-closed, dual-closed class of multi-path matroids is introduced, a polynomial-time algorithm for computing the TuttePolynomial of a multi- path matroid is given, their basis activities are described, and some basic structural properties are proved.

Forests, colorings and acyclic orientations of the square lattice

Some asymptotic counting results about these quantities on then ×n section of the square lattice are obtained together with some properties of the structure of the random forest.

Spanning trees and orientations of graphs

A conjecture of Merino and Welsh says that the number of spanning trees τ (G) of a loopless and bridgeless multigraph G is always less than or equal to either the number a(G) of acyclic orientations,