1Department of Mathematics, Indian Institute of Technology Patna
Acta mathematica Universitatis Comenianae, Tome 83 (2014) no. 2, pp. 157-163
Citer cet article
Ram Krishna Pandey; Ram Krishna Pandey. A note on the equivalence of Motzskin's maximal density and Ruzsa's measures of intersectivity. Acta mathematica Universitatis Comenianae, Tome 83 (2014) no. 2, pp. 157-163. http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a0/
@article{AMUC_2014_83_2_a0,
author = {Ram Krishna Pandey and Ram Krishna Pandey},
title = { A note on the equivalence of {Motzskin's} maximal density and {Ruzsa's} measures of intersectivity},
journal = {Acta mathematica Universitatis Comenianae},
pages = {157--163},
year = {2014},
volume = {83},
number = {2},
url = {http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a0/}
}
TY - JOUR
AU - Ram Krishna Pandey
AU - Ram Krishna Pandey
TI - A note on the equivalence of Motzskin's maximal density and Ruzsa's measures of intersectivity
JO - Acta mathematica Universitatis Comenianae
PY - 2014
SP - 157
EP - 163
VL - 83
IS - 2
UR - http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a0/
ID - AMUC_2014_83_2_a0
ER -
%0 Journal Article
%A Ram Krishna Pandey
%A Ram Krishna Pandey
%T A note on the equivalence of Motzskin's maximal density and Ruzsa's measures of intersectivity
%J Acta mathematica Universitatis Comenianae
%D 2014
%P 157-163
%V 83
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_2014_83_2_a0/
%F AMUC_2014_83_2_a0
In this short note, we see the equivalence of Motzkin's maximal density of integral sets whose no two elements are allowed to differ by an element of a given set $M$ of positive integers and the measures of difference intersectivity defined by Ruzsa. Further more, the maximal density $\mu(M)$has been determined for some infinite sets $M$ and in a specific case of generalized arithmetic progression of dimension two a lower bound has been given for $\mu(M)$.
