Random matroids

Kordecki Wojciech

GDML_Books, (1997), p.

Résumé

CONTENTS1. Introduction.............................................................................52. Matroids..................................................................................6  2.1. Notations and basic properties...........................................6  2.2. Gaussian coefficients.......................................................10  2.3. Projective geometries.......................................................11  2.4. Special classes................................................................143. Probabilistic tools..................................................................15  3.1. Poisson convergence.......................................................15  3.2 Normal convergence.........................................................17  3.3. Markov processes on finite lattices..................................184. Random matroids - general approach..................................19  4.1. Definitions........................................................................19  4.2. Rank.................................................................................21  4.3. Duality..............................................................................235. Random projective geometries - combinatorial results..........26  5.1. Distribution of rank...........................................................26  5.2. Fullsubspaces - expectation and variance.......................30  5.3. Submatroids of a given type............................................336. Random projective geometries - limit theorems....................33  6.1. Rank of random subspaces.............................................33  6.2. Small submatroids...........................................................38  6.3. Full subspaces................................................................43  6.4. Related results................................................................467. Problems and conclusions....................................................49Appendix: tables.......................................................................49  1. Gaussian coefficients.........................................................49  2. Probabilities $P^{(r)}$.........................................................51  3. Parameters of X..................................................................53Bibliography..............................................................................54

1991 Mathematics Subject Classification: Primary 05B35; Secondary 60C05.

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EUDML-ID : urn:eudml:doc:271749