We show that if $A$ is a subset of a group of prime order $p$ such that $|2A|<2.7652|A|$ and $|A|<1.25\cdot10^{-6}p$, then $A$ is contained in an arithmetic progression with at most $|2A|-|A|+1$ terms, and $2A$ contains an arithmetic progression with the same difference and at least $2|A|-1$ terms. This improves a number of previously known results towards the conjectured value $3|A|-4$ for which such an statement should hold..
@article{10_37236_11976,
author = {Vsevolod F. Lev and Oriol Serra},
title = {Towards \(3n-4\) in groups of prime order},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {2},
doi = {10.37236/11976},
zbl = {1528.11105},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11976/}
}
TY - JOUR
AU - Vsevolod F. Lev
AU - Oriol Serra
TI - Towards \(3n-4\) in groups of prime order
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/11976/
DO - 10.37236/11976
ID - 10_37236_11976
ER -
%0 Journal Article
%A Vsevolod F. Lev
%A Oriol Serra
%T Towards \(3n-4\) in groups of prime order
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/11976/
%R 10.37236/11976
%F 10_37236_11976
Vsevolod F. Lev; Oriol Serra. Towards \(3n-4\) in groups of prime order. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11976
