Vol. 8, No. 2, 2015

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN (electronic): 1944-4184
ISSN (print): 1944-4176
 
Author index
To appear
 
Other MSP journals
Crossings of complex line segments

Samuli Leppänen

Vol. 8 (2015), No. 2, 285–294
Abstract

The crossing lemma holds in 2 because a real line separates the plane into two disjoint regions. In 2 removing a complex line keeps the remaining point-set connected. We investigate the crossing structure of affine line segment-like objects in 2 by defining two notions of line segments between two points and give computational results on combinatorics of crossings of line segments induced by a set of points. One way we define the line segments motivates a related problem in 3, which we introduce and solve.

Keywords
discrete geometry, crossing inequality
Mathematical Subject Classification 2010
Primary: 51M05, 51M30, 52C35
Secondary: 51M04
Milestones
Received: 16 July 2013
Revised: 22 February 2014
Accepted: 23 February 2014
Published: 3 March 2015

Communicated by Kenneth S. Berenhaut
Authors
Samuli Leppänen
Department of Mathematics
University of British Columbia
Vancouver BC V6T 1Z2
Canada