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Typical structure of hereditary properties of binary matroids
Stefan Grosser, Hamed Hatami, Peter Nelson +1
We prove an arithmetic analogue of the typical structure theorem for graph hereditary properties due to Alon, Balogh, Bollobás and Morris.
The critical number of -free triangle-free binary matroids
Peter Nelson, Kazuhiro Nomoto
A simple binary matroid, viewed as a restriction of a finite binary projective geometry , is -free if for any rank- flat of , its intersection wit…
The smallest -free and triangle-free binary matroids
Peter Nelson, Kazuhiro Nomoto
We determine the smallest simple triangle-free binary matroids that have no five-element independent flat. This solves a special case of a conjecture of Nelson and Norin.
The structure of -free and triangle-free binary matroids
Peter Nelson, Kazuhiro Nomoto
A simple binary matroid is called -free if none of its rank-4 flats are independent sets. These objects can be equivalently defined as the sets of points in fo…
The smallest matroids with no large independent flat
Peter Nelson, Sergey Norin
We show that a simple rank- matroid with no -element independent flat has at least as many elements as the matroid defined as the direct sum of binary proje…
The structure of claw-free binary matroids
Peter Nelson, Kazuhiro Nomoto
A simple binary matroid is called claw-free if none of its rank-3 flats are independent sets. These objects can be equivalently defined as the sets of points in $\mathrm{PG}(n-…