Sequences of Integers with Missing Quotients and Dense Points Without Neighbors

Details Sequences of Integers with Missing Quotients and Dense Points Without Neighbors Sequences of Integers with Missing Quotients and Dense Points Without Neighbors

2011-04-04

arxiv.org/abs/1104.0441v1

Mathematics

Combinatorics

20 pages, 4 figures

Scientific paper

Let A be a pre-defined set of rational numbers. We say a set of natural numbers S is an A-quotient-free set if no ratio of two elements in S belongs to A. We find the maximal asymptotic density and the maximal upper asymptotic density of A-quotient-free sets when A belongs to a particular class. It is known that in the case A = {p, q}, where p, q are coprime integers greater than one, the latest problem is reduced to evaluation of the largest number of lattice non-adjacent points in a triangle whose legs lie on coordinate axis. We prove that this number is achieved by choosing points of the same color in the checkerboard coloring.

Affiliated with

Also associated with

No associations

Rating

Sequences of Integers with Missing Quotients and Dense Points Without Neighbors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sequences of Integers with Missing Quotients and Dense Points Without Neighbors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sequences of Integers with Missing Quotients and Dense Points Without Neighbors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-316974