Elementary proof techniques for the maximum number of islands

Details Elementary proof techniques for the maximum number of islands Elementary proof techniques for the maximum number of islands

2009-10-24

arxiv.org/abs/0910.4647v1

Mathematics

Combinatorics

11 pages, 5 figures, submitted on March 31

Scientific paper

Islands are combinatorial objects that can be intuitively defined on a board consisting of a finite number of cells. Based on the neighbor relation of the cells, it is a fundamental property that two islands are either containing or disjoint. Recently, numerous extremal questions have been answered using different methods. We show elementary techniques unifying these approaches. Our building parts are based on rooted binary trees and discrete geometry. Among other things, we show the maximum cardinality of islands on a toroidal board and in a hypercube. We also strengthen a previous result by rarefying the neighborhood relation.

Affiliated with

Also associated with

No associations

Rating

Elementary proof techniques for the maximum number of islands 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 Elementary proof techniques for the maximum number of islands, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Elementary proof techniques for the maximum number of islands will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-211699