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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.
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This content will become publicly available on January 1, 2026
Introduction to “Re-situations of Scientific Knowledge: A Case Study of a Skirmish Over Clusters vs Clines in Human Population Genomics”
The analysis in this chapter focuses on how life scientists working in the field of human population genomics ancestry studies (HPGA) produce and re-use scientific knowledge (see Griesemer and Barragán 2022, Chap. 24 in this volume).
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- Award ID(s):
- 1849307
- PAR ID:
- 10632014
- Editor(s):
- Ankeny, Rachel A; Dietrich, Michael R; Leonelli, Sabina
- Publisher / Repository:
- Springer Nature Switzerland
- Date Published:
- Edition / Version:
- 1
- ISBN:
- 978-3-031-84608-3
- Page Range / eLocation ID:
- 359-363
- Subject(s) / Keyword(s):
- History, Philosophy, Social Studies of Science
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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