# Questions tagged [matroid-theory]

Questions related to the field of Combinatorics called Matroid Theory. Relevant topics include matroids in Combinatorial Optimization, Lattice Theory, Algebraic Geometry, Polyhedral Theory, Rigidity, and Algorithms. For questions about Oriented Matroids, the oriented-matroids tag may be used.

**11**

**3**answers

### Log-concavity of matroids: characterization of equality?

**5**

**0**answers

### What do the circuits of this matroid look like?

**2**

**1**answer

### Fast sampling of matroids

**8**

**1**answer

### A Hadamard product of binary (or ternary) matroids

**0**

**1**answer

### Prove that a definition of $\mathcal{I}$ does not satisfy the exchange property

**1**

**0**answers

### Basis exchange property proof without use of rank and span

**3**

**1**answer

### Does every geometric lattice of rank $r$ contain the Boolean $B_r$ as a sublattice?

**8**

**1**answer

### p-adic versions of log concavity for graphs (or matroids)

**2**

**0**answers

### What's known about the matroid induced by the Plücker coordinates of the representation of a matroid?

**7**

**2**answers

### Constructing a $0/1$ polytope from an abstract simplicial complex

**3**

**2**answers

### Open problems in matroid theory

**3**

**2**answers

### Inequality of $h$-vectors of shellable simplicial complexes

**1**

**0**answers

### Cohomology of realization space of matroid

**6**

**1**answer

### Does the purported proof of Rota's conjecture provide an algorithm for calculating the forbidden minors of matroids over arbitrary finite fields?

**14**

**1**answer

### Another characterization of matroids

**4**

**1**answer

### What is the significance of ear decompositions for non-graphic matroids?

**5**

**1**answer

### Exchanges between independent sets of a matroid

**5**

**1**answer

### Minimum number of independent pairs in a matroid

**3**

**2**answers

### When do the circuits of a matroid have a connected intersection graph?

**11**

**0**answers

### Existence of a strong antichain

**15**

**3**answers

### Is matroid realizability computable?

**2**

**1**answer

### Extending spanning sets on contractions of matroids

**11**

**1**answer

### Is there Matrix-Tree theorem for counting the bases of a connected matroid?

**7**

**1**answer

### Combinatorial meaning of Kazhdan-Lusztig-Stanley polynomial

**2**

**0**answers

### The best way for obtaining the canonical label of a matroid?

**5**

**0**answers

### Set-theoretic generation by circuit polynomials

**4**

**0**answers

### Maximal number of smallest circuits in a matroid

**0**

**0**answers

### what kind of functions can be optimized over matroid polytope

**5**

**1**answer

### Extending submodular functions from a sublattice

**10**

**1**answer

### Poset-troids …?

**2**

**1**answer

### Upper-bounding $\dim \text{span}\{v_1,\dots,v_n\}$ in terms of $\dim \text{span}$ of subsets

**1**

**0**answers

### Matroids with no relaxations (~ weak maps)

**2**

**2**answers

### How to generating all flats of the cycle matroid of a graph?

**4**

**0**answers

### Understanding this example of projective geometry in Algebraic matroids

**12**

**2**answers

### Does the basis graph of a matroid determine it?

**2**

**0**answers

### Reference request: Matroid cryptomorphisms for arbitrary monomial ideals

**0**

**0**answers

### Paths in graphs as a vector space or matroid

**0**

**1**answer

### How to find all minimal dependent sets of a set of vectors effectively?

**1**

**1**answer

### From Steiner systems to geometric lattices to matroids

**1**

**2**answers

### Mapping of subcubes of a $(d+k)$-hypercube onto subcubes of a $d$-hypercube

**3**

**0**answers

### Matroids which are transitive on minimal basis exchanges

**5**

**0**answers

### Disjoint Common Transversals of Two Families of Sets

**5**

**1**answer

### Do the Odd Cycles of a Graph Define a Matroid?

**5**

**1**answer

### Toggles for non-broken-circuit sets in matroids

**1**

**1**answer

### A new generalisation of dimension? part 2

**1**

**0**answers

### When does a collection of sets forming a geometric lattice give the flats of a matroid?

**6**

**1**answer

### Name of a binary matroid coming from the cycle space of a graph

**10**

**0**answers

### Fundamental circuit characterization of matroid independence complexes

**5**

**1**answer

### Greedy simplices in an ultrametric space (generalized Bhargava $p$-orderings)

**6**

**1**answer