Vol. 8, No. 1, 2015

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

Volume 12
Issue 5, 721–899
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

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
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
Author Index
Coming Soon
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Other MSP Journals
This article is available for purchase or by subscription. See below.
A note on triangulations of sumsets

Károly J. Böröczky and Benjamin Hoffman

Vol. 8 (2015), No. 1, 75–85

For finite subsets A and B of 2, we write A + B = {a + b : a A,b B}. We write tr(A) to denote the common number of triangles in any triangulation of the convex hull of A using the points of A as vertices. We consider the conjecture that tr(A + B)1 2 tr(A)1 2 + tr(B)1 2 . If true, this conjecture would be a discrete two-dimensional analogue to the Brunn–Minkowski inequality. We prove the conjecture in three special cases.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

additive combinatorics, sumsets, Brunn–Minkowski inequality, triangulations
Mathematical Subject Classification 2010
Primary: 11B75, 52C05
Received: 28 December 2012
Revised: 31 May 2013
Accepted: 22 September 2013
Published: 10 December 2014

Communicated by Andrew Granville
Károly J. Böröczky
Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences
Reáltanoda utca 13-15
Budapest 1053
Central European University
1051 Budapest, Nádor utca 9
Benjamin Hoffman
Department of Mathematical Sciences
Lewis & Clark College
615 Palatine Hill Road
Portland, OR 97219
United States