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DM
1998
195views more  DM 1998»
13 years 4 months ago
On basis-exchange properties for matroids
We give a counterexample to a conjecture by Wild about binary matroids. We connect two equivalent lines of research in matroid theory: a simple type of basis-exchange property and ...
Joseph E. Bonin
JCT
2010
113views more  JCT 2010»
13 years 3 months ago
Equations resolving a conjecture of Rado on partition regularity
A linear equation L is called k-regular if every k-coloring of the positive integers contains a monochromatic solution to L. Richard Rado conjectured that for every positive intege...
Boris Alexeev, Jacob Tsimerman