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=\lfloor n/2 \rfloor . 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.
https://hal.inria.fr/hal-00958981
Contributeur : Service Ist Inria Sophia Antipolis-Méditerranée / I3s
<>
Soumis le : jeudi 13 mars 2014 - 16:56:00
Dernière modification le : mercredi 29 novembre 2017 - 10:26:19
Document(s) archivé(s) le : vendredi 13 juin 2014 - 12:07:56
W. M. B. Dukes. On a Unimodality Conjecture in Matroid Theory. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2002, 5, pp.181-190. 〈hal-00958981〉
