Consecutive integers in high-multiplicity sumsets
| dc.creator | Lev, Vsevolod F. | |
| dc.date | 2008-06-27 | |
| dc.date.accessioned | 2026-07-07T09:47:14Z | |
| dc.date.available | 2026-07-07T09:47:14Z | |
| dc.description | Sharpening (a particular case of) a result of Szemeredi and Vu and extending earlier results of Sarkozy and ourselves, we find, subject to some technical restrictions, a sharp threshold for the number of integer sets needed for their sumset to contain a block of consecutive integers of length, comparable with the lengths of the set summands. A corollary of our main result is as follows. Let $k,l\ge 1$ and $n\ge 3$ be integers, and suppose that $A_1,...,A_k\subset[0,l]$ are integer sets of size at least $n$, none of which is contained in an arithmetic progression with difference greater than 1. If $k\ge 2\lceil(l-1)/(n-2)\rceil$, then the sumset $A_1+...+A_k$ contains a block of consecutive integers of length $k(n-1)$. | |
| dc.description | Nine pages | |
| dc.identifier | https://arxiv.org/abs/0806.4580 | |
| dc.identifier | http://arxiv.org/abs/0806.4580 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163799 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.title | Consecutive integers in high-multiplicity sumsets | |
| dc.type | text |