<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper we study the conditions (1), (2) and (3) for the permutations which preserve the weighted density. These conditions are motivated by the conditions of Lévy group, originated in [Levy, P.: Problèmes concrets d’Analyse Fonctionelle. Gauthier Villars, Paris, 1951], and studied in [Obata, N.: Density of natural numbers and Lévy group, J. Number Theory <bold>30 </bold>(1988), 288-297]. In the second part we prove that under some conditions for the sequence of weights, for instance for the logarithmic density, the first two conditions can be launched</p></abstract>

In this paper we study the conditions (1), (2) and (3) for the permutations which preserve the weighted density. These conditions are motivated by the conditions of Lévy group, originated in [Levy, P.: Problèmes concrets d’Analyse Fonctionelle. Gauthier Villars, Paris, 1951], and studied in [Obata, N.: Density of natural numbers and Lévy group, J. Number Theory 30 (1988), 288-297]. In the second part we prove that under some conditions for the sequence of weights, for instance for the logarithmic density, the first two conditions can be launched

SOME REMARKS ON PERMUTATIONS WHICH PRESERVE THE WEIGHTED DENSITY

Tatra Mountains Mathematical Publications

{"article-title":"SOME REMARKS ON PERMUTATIONS WHICH PRESERVE THE WEIGHTED DENSITY"}

In this paper we study the conditions (1), (2) and (3) for the permutations which preserve the weighted density. These conditions are motivated by the...

SOME REMARKS ON PERMUTATIONS WHICH PRESERVE THE WEIGHTED DENSITY

Published Online: Feb 18, 2014

Page range: 35 - 45

DOI: https://doi.org/10.2478/tmmp-2013-0024

Keywords
weighted density, permutation, Levy group

This content is open access.

SOME REMARKS ON PERMUTATIONS WHICH PRESERVE THE WEIGHTED DENSITY

Published Online: Feb 18, 2014

Page range: 35 - 45

DOI: https://doi.org/10.2478/tmmp-2013-0024

Keywordsweighted density, permutation, Levy group

This content is open access.

Keywords
weighted density, permutation, Levy group