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### 0/1 Borsuk Problems on Matroids

**Algebra & Discrete Mathematics**

Speaker: | Gyivan Lopez-Campos, National University of Mexico (UNAM) |

Location: | 1147 Math. Sci. Building |

Start time: | Fri, Oct 25 2024, 3:10PM |

The Borsuk partition problem or better known as the Borsuk Conjecture asks whether for all $S \subset R^n$ 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 $S$ has 0 and 1 entries only. The Borsuk problem restricted to this type of binary sets is known today as the 0/1-Borsuk problem. In this talk, we are going to analyze this counterexample and the 0/1-Borsuk problem when the set is the set of vertices of a matroid basis polytope.