Random matroids

Kordecki Wojciech. Random matroids. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1997. <http://eudml.org/doc/271749>.

@book{KordeckiWojciech1997,
abstract = {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..............................................................................541991 Mathematics Subject Classification: Primary 05B35; Secondary 60C05.},
author = {Kordecki Wojciech},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Random matroids},
url = {http://eudml.org/doc/271749},
year = {1997},
}

TY - BOOK
AU - Kordecki Wojciech
TI - Random matroids
PY - 1997
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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..............................................................................541991 Mathematics Subject Classification: Primary 05B35; Secondary 60C05.
LA - eng
UR - http://eudml.org/doc/271749
ER -