Exact Expectation and Variance of Minimal Basis of Random Matroids
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 2, p. 277.

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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).
Classification : 05C31, 05C80, 05B35
Mots-clés : minimal basis, q-analog, finite projective geometry, Tutte polynomial, -analog 
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Wojciech Kordecki; Anna Lyczkowska-Hanćkowiak. Exact Expectation and Variance of Minimal Basis of Random Matroids. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 2, p. 277. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_2_267680/