Open Access
Translator Disclaimer
2015 A note on triangulations of sumsets
Károly Böröczky, Benjamin Hoffman
Involve 8(1): 75-85 (2015). DOI: 10.2140/involve.2015.8.75

Abstract

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.

Citation

Download Citation

Károly Böröczky. Benjamin Hoffman. "A note on triangulations of sumsets." Involve 8 (1) 75 - 85, 2015. https://doi.org/10.2140/involve.2015.8.75

Information

Received: 28 December 2012; Revised: 31 May 2013; Accepted: 22 September 2013; Published: 2015
First available in Project Euclid: 22 November 2017

zbMATH: 1310.11014
MathSciNet: MR3321712
Digital Object Identifier: 10.2140/involve.2015.8.75

Subjects:
Primary: 11B75 , 52C05

Keywords: additive combinatorics , Brunn–Minkowski inequality , sumsets , triangulations

Rights: Copyright © 2015 Mathematical Sciences Publishers

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.8 • No. 1 • 2015
MSP
Back to Top