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0/1-Borsuk problem on matroids
Algebra & Discrete Mathematics| Speaker: | Gyivan Lopez-Campos, National University of Mexico |
| Location: | 1147 MSB |
| Start time: | Fri, Oct 11 2024, 3:00PM |
The Borsuk partition problem or better known as the Borsuk Conjecture asks whether for all $S ⊂ R^n$ with diameter $d$, there is a partition of $S$ in at most $n + 1$ subsets such that the diameter of each subset is less than $d$.
In 1993, the conjecture was proved false by J. Kahn and G. Kalai, with an astonishing finite conterexample, furthermore, the given set has 0 and 1 coordinates. The Borsuk problem restricted to this type of sets is known today as the 0/1-Borsuk problem.
In this talk, we are going to analyze their counterexample and the 0/1-Borsuk problem when the set is the set of vertices of a matroid basis polytope.