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.
|Number of pages||10|
|Journal||Discrete Mathematics and Theoretical Computer Science|
|Publication status||Published - 2002|
- matroid theory
- unimodal conjecture
- rank 2 matroids
- rank 3 matroids