@inproceedings{ce1d9cc3e1bd403bb45a2fb05b11d7a2,

title = "Arithmetic progressions in sumsets of sparse sets",

abstract = "A set of positive integers A 0 is log-sparse if there is an absolute constant C so that for any positive integer x the sequence contains at most C elements in the interval [x, 2x). In this note, we study arithmetic progressions in sums of logsparse subsets of 0. We prove that for any log-sparse subsets S1, Sn of 0, the sumset S = S1 + Sn cannot contain an arithmetic progression of size greater than n(1+o(1))n. We also show that this is nearly tight by proving that there exist log-sparse sets S1, Sn such that S1 + Sn contains an arithmetic progression of size n(1-o(1))n.",

author = "Noga Alon and Ryan Alweiss and Liu, {Yang P.} and Anders Martinsson and Shyam Narayanan",

note = "Publisher Copyright: {\textcopyright} 2022 Walter de Gruyter GmbH, Berlin/Boston.",

year = "2022",

month = apr,

day = "19",

doi = "10.1515/9783110754216-003",

language = "English (US)",

series = "De Gruyter Proceedings in Mathematics",

publisher = "Walter de Gruyter GmbH",

pages = "27--33",

editor = "Landman, {Bruce M.} and Florian Luca and Nathanson, {Melvyn B.} and Jaroslav Nesetril and Aaron Robertson",

booktitle = "Number Theory and Combinatorics - A Collection in Honor of the Mathematics of Ronald Graham",

address = "Germany",

}