## 11 Citations

### Lattice path matroids and quotients

- MathematicsArXiv
- 2022

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

- MathematicsDiscret. Comput. Geom.
- 2018

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

- MathematicsDiscrete & Computational Geometry
- 2018

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

- Mathematics
- 2016

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

- Mathematics
- 2022

. 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

- Mathematics, Computer SciencePhysica A: Statistical Mechanics and its Applications
- 2020

### Study of Exponential Growth Constants of Directed Heteropolygonal Archimedean Lattices

- Computer ScienceJournal of Statistical Physics
- 2019

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

- MathematicsDiscrete & 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

### Lattice path matroids: enumerative aspects and Tutte polynomials

- MathematicsJ. Comb. Theory, Ser. A
- 2003

### Computing the Tutte polynomial of lattice path matroids using determinantal circuits

- Computer Science, MathematicsTheor. Comput. Sci.
- 2015

### Lattice Path Matroid Polytopes

- Mathematics
- 2012

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

- MathematicsComb.
- 2010

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

- Mathematics
- 2015

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…

### Multi-Path Matroids

- Mathematics, Computer ScienceCombinatorics, Probability and Computing
- 2007

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

- Mathematics, Computer Science
- 1999

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

- Mathematics
- 2010

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,…