skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Formation of a giant component in the intersection graph of a random chord diagram
Award ID(s):
1502650
PAR ID:
10077518
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of Combinatorial Theory, Series B
Volume:
125
Issue:
C
ISSN:
0095-8956
Page Range / eLocation ID:
33 to 79
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
  2. In this paper we show that every set A⊂ℕ with positive density contains B+C for some pair B,C of infinite subsets of ℕ, settling a conjecture of Erd\H os. The proof features two different decompositions of an arbitrary bounded sequence into a structured component and a pseudo-random component. Our methods are quite general, allowing us to prove a version of this conjecture for countable amenable groups. 
    more » « less