Dukes, W.M.B. (2002) On a unimodality conjecture in matroid theory. Discrete Mathematics and Theoretical Computer Science, 5 (1). pp. 181-190. ISSN 1365-8050Full text not available in this repository. Request a copy from the Strathclyde author
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.
|Keywords:||matroid theory, unimodal conjecture, rank 2 matroids, rank 3 matroids, Electronic computers. Computer science, Discrete Mathematics and Combinatorics, Theoretical Computer Science, Computer Science(all)|
|Subjects:||Science > Mathematics > Electronic computers. Computer science|
|Department:||Faculty of Science > Computer and Information Sciences|
|Depositing user:||Pure Administrator|
|Date Deposited:||10 Dec 2014 11:52|
|Last modified:||03 Apr 2017 00:07|