Exact Expectation and Variance of Minimal Basis of Random Matroids

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....

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Main Authors:	Kordecki Wojciech, Lyczkowska-Hanćkowiak Anna
Format:	Article
Language:	English
Published:	Sciendo 2013-05-01
Series:	Discussiones Mathematicae Graph Theory
Subjects:	minimal basis q-analog finite projective geometry tutte polynomial
Online Access:	https://doi.org/10.7151/dmgt.1662

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spelling	doaj-d04e07e5b4b740739323cc4fc0b840132021-09-05T17:20:19ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922013-05-0133227728810.7151/dmgt.1662Exact Expectation and Variance of Minimal Basis of Random MatroidsKordecki Wojciech0Lyczkowska-Hanćkowiak Anna1University of Business in Wroclaw Department of Management ul. Ostrowskiego 22, 53-238 Wroclaw, PolandPoznán University of Economics Faculty of Informatics and Electronic Economy Department of Operations Research al. Niepodleg lo´sci 10, 61-875 Poznán, PolandWe 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).https://doi.org/10.7151/dmgt.1662minimal basisq-analogfinite projective geometrytutte polynomial
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Kordecki Wojciech Lyczkowska-Hanćkowiak Anna
spellingShingle	Kordecki Wojciech Lyczkowska-Hanćkowiak Anna Exact Expectation and Variance of Minimal Basis of Random Matroids Discussiones Mathematicae Graph Theory minimal basis q-analog finite projective geometry tutte polynomial
author_facet	Kordecki Wojciech Lyczkowska-Hanćkowiak Anna
author_sort	Kordecki Wojciech
title	Exact Expectation and Variance of Minimal Basis of Random Matroids
title_short	Exact Expectation and Variance of Minimal Basis of Random Matroids
title_full	Exact Expectation and Variance of Minimal Basis of Random Matroids
title_fullStr	Exact Expectation and Variance of Minimal Basis of Random Matroids
title_full_unstemmed	Exact Expectation and Variance of Minimal Basis of Random Matroids
title_sort	exact expectation and variance of minimal basis of random matroids
publisher	Sciendo
series	Discussiones Mathematicae Graph Theory
issn	2083-5892
publishDate	2013-05-01
description	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).
topic	minimal basis q-analog finite projective geometry tutte polynomial
url	https://doi.org/10.7151/dmgt.1662
work_keys_str_mv	AT kordeckiwojciech exactexpectationandvarianceofminimalbasisofrandommatroids AT lyczkowskahanckowiakanna exactexpectationandvarianceofminimalbasisofrandommatroids
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Exact Expectation and Variance of Minimal Basis of Random Matroids

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