The Smallest Matroids with no Large Independent Flat
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.
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2019 ◽
Vol 31
(08)
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pp. 1950026
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2013 ◽
Vol 89
(2)
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pp. 234-242
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2002 ◽
Vol 31
(2)
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pp. 97-101
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2019 ◽
Vol 18
(02)
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pp. 1950035
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1980 ◽
Vol 16
(3)
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pp. 265-273
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