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
842 48 Bratislava, Slovak Republic
Telephone: + 421-2-60295111 Fax: + 421-2-65425882
e-Mail: email@example.com Internet: www.iam.fmph.uniba.sk/amuc
© 2013, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE