A note on the equivalence of Motzkin's maximal density and Rusza's measures of intersectivity
R. K. Pandey Received: December 28, 2012;
Revised: October 19, 2013;
Accepted: February 19, 2014
Abstract.
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 μ(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
μ(M).
Keywords:
upper asymptotic density; maximal density; generalized arithmetic progression.
AMS Subject classification:
Primary: 11B05
Version to read:
PDF ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2013, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |