The Smallest Matroids with no Large Independent Flat
- 14 January 2021
- journal article
- research article
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 28 (1), P1.31
- https://doi.org/10.37236/8992
Abstract
We show that a simple rank-$r$ matroid with no $(t+1)$-element independent flat has at least as many elements as the matroid $M_{r,t}$ defined to be the direct sum of $t$ binary projective geometries whose ranks pairwise differ by at most $1$. We also show for $r \geqslant 2t$ that $M_{r,t}$ is the unique example for which equality holds.
Keywords
This publication has 1 reference indexed in Scilit:
- Lectures on matroidsJournal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics, 1965