Abstract
A certain unimodal conjecture in matroid theory states the number of rank-r matroids on a set of size n is unimodal in r and attains its maximum at r=⌊ n/2 ⌋. We show that this conjecture holds up to r=3 by constructing a map from a class of rank-2 matroids into the class of loopless rank-3 matroids. Similar inequalities are proven for the number of non-isomorphic loopless matroids, loopless matroids and matroids.
| Original language | English |
|---|---|
| Pages (from-to) | 181-190 |
| Number of pages | 10 |
| Journal | Discrete Mathematics and Theoretical Computer Science |
| Volume | 5 |
| Issue number | 1 |
| Publication status | Published - 2002 |
Keywords
- matroid theory
- unimodal conjecture
- rank 2 matroids
- rank 3 matroids