Geodesic
On a Unimodality Conjecture in Matroid Theory
Discrete mathematics & theoretical computer science, Tome 5 (2002).

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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. 
@article{DMTCS_2002_5_a13,
     author = {Dukes, W. M. B.},
     title = {On a {Unimodality} {Conjecture} in {Matroid} {Theory}},
     journal = {Discrete mathematics & theoretical computer science},
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     doi = {10.46298/dmtcs.307},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.307/}
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Dukes, W. M. B. On a Unimodality Conjecture in Matroid Theory. Discrete mathematics & theoretical computer science, Tome 5 (2002). doi : 10.46298/dmtcs.307. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.307/

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