Exact expectation and variance of minimal basic of random matroids
Wojciech Kordecki, Anna Łyczkowska-Hanćkowiak · Discussiones Mathematicae Graph Theory · 2012
We formulate and prove a formula to compute the expected value of the minimal random basis of an arbitrary finite matroid whose elements are assigned weights which are independent and uniformly distributed on the interval [0, 1]. This method yields an exact formula in terms of the Tutte polynomial. We give a simple formula to find the minimal random basis of the projective geometry PG(r − 1, q).