An approximate structure theorem for small sumsets
Let A and B be randomly chosen s-subsets of the first n integers such that their sumset A+B has size at most Ks. We show that asymptotically almost surely A and B are almost fully contained in arithmetic progressions PA and PB with the same common difference and cardinalities approximately Ks/2. The...
| Authors: | , , , |
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| Format: | book part |
| Publication Date: | 2021 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/369273 |
| Online Access: | https://hdl.handle.net/2117/369273 https://dx.doi.org/10.1007/978-3-030-83823-2_88 |
| Access Level: | Open access |
| Keyword: | Sequences (Mathematics) Additive combinatorics Sumsets Hypergraph containers Successions (Matemàtica) Classificació AMS::11 Number theory::11B Sequences and sets Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
| Summary: | Let A and B be randomly chosen s-subsets of the first n integers such that their sumset A+B has size at most Ks. We show that asymptotically almost surely A and B are almost fully contained in arithmetic progressions PA and PB with the same common difference and cardinalities approximately Ks/2. The result holds for s=¿(log3n) and 2=K=o(s/log3n). Our main tool is an asymmetric version of the method of hypergraph containers which was recently used by Campos to prove the result in the special case A=B. |
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