Exact site frequency spectra of neutrally evolving tumors: A transition between power laws reveals a signature of cell viability
- Award ID(s):
- 2052465
- PAR ID:
- 10326506
- Date Published:
- Journal Name:
- Theoretical Population Biology
- Volume:
- 142
- Issue:
- C
- ISSN:
- 0040-5809
- Page Range / eLocation ID:
- 67 to 90
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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.more » « less
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