Friedrich Bormann: Formulas and Fairness in Matroid Bingo

Supervisor: Benjamin Schröter
Abstract: In my presentation I introduce matroids via a variation of the game bingo. We establish formulas to compute winning probabilities in the spacial classes of elementary split and cuspidal matroids. To prove these formulas, we use geometric properties of the base polytope of a matroid as well as direct combinatorial arguments. Furthermore, we present a constructive method to generate arbitrary large equitable matroids. Finally, we discuss how one could use the developed formulas to obtain an equitable matroid with circuits of different lengths.