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Unfair permutations

We study unfair permutations, which are generated by letting [Formula: see text] players draw numbers and assuming that player [Formula: see text] draws [Formula: see text] times from the unit interval and records her largest value. This model is natural in the context of partitions: the score of th...

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Detalles Bibliográficos
Autores principales: Prodinger, Helmut, Schneider, Carsten, Wagner, Stephan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2011
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4819032/
https://www.ncbi.nlm.nih.gov/pubmed/27087722
http://dx.doi.org/10.1016/j.ejc.2011.04.002
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author Prodinger, Helmut
Schneider, Carsten
Wagner, Stephan
author_facet Prodinger, Helmut
Schneider, Carsten
Wagner, Stephan
author_sort Prodinger, Helmut
collection PubMed
description We study unfair permutations, which are generated by letting [Formula: see text] players draw numbers and assuming that player [Formula: see text] draws [Formula: see text] times from the unit interval and records her largest value. This model is natural in the context of partitions: the score of the [Formula: see text] th player corresponds to the multiplicity of the summand [Formula: see text] in a random partition, with the roles of minimum and maximum interchanged. We study the distribution of several parameters, namely the position of player [Formula: see text] , the number of inversions, and the number of ascents. To perform some of the heavy computations, we use the computer algebra package Sigma.
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spelling pubmed-48190322016-04-14 Unfair permutations Prodinger, Helmut Schneider, Carsten Wagner, Stephan Eur J Comb Article We study unfair permutations, which are generated by letting [Formula: see text] players draw numbers and assuming that player [Formula: see text] draws [Formula: see text] times from the unit interval and records her largest value. This model is natural in the context of partitions: the score of the [Formula: see text] th player corresponds to the multiplicity of the summand [Formula: see text] in a random partition, with the roles of minimum and maximum interchanged. We study the distribution of several parameters, namely the position of player [Formula: see text] , the number of inversions, and the number of ascents. To perform some of the heavy computations, we use the computer algebra package Sigma. Elsevier 2011-11 /pmc/articles/PMC4819032/ /pubmed/27087722 http://dx.doi.org/10.1016/j.ejc.2011.04.002 Text en © 2011 Elsevier Ltd. https://creativecommons.org/licenses/by-nc-nd/3.0/This is an open access article under the CC BY NC ND license (https://creativecommons.org/licenses/by-nc-nd/3.0/).
spellingShingle Article
Prodinger, Helmut
Schneider, Carsten
Wagner, Stephan
Unfair permutations
title Unfair permutations
title_full Unfair permutations
title_fullStr Unfair permutations
title_full_unstemmed Unfair permutations
title_short Unfair permutations
title_sort unfair permutations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4819032/
https://www.ncbi.nlm.nih.gov/pubmed/27087722
http://dx.doi.org/10.1016/j.ejc.2011.04.002
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