The structure of maximum subsets of \(\{1,\dots,n\}\) with no solutions to \(a+b=kc\)
The electronic journal of combinatorics, Tome 12 (2005)
If $k$ is a positive integer, we say that a set $A$ of positive integers is $k$-sum-free if there do not exist $a,b,c$ in $A$ such that $a + b = kc$. In particular we give a precise characterization of the structure of maximum sized $k$-sum-free sets in $\{1,\ldots,n\}$ for $k\ge 4$ and $n$ large.
@article{10_37236_1916,
author = {Andreas Baltz and Peter Hegarty and Jonas Knape and Urban Larsson and Tomasz Schoen},
title = {The structure of maximum subsets of \(\{1,\dots,n\}\) with no solutions to \(a+b=kc\)},
journal = {The electronic journal of combinatorics},
year = {2005},
volume = {12},
doi = {10.37236/1916},
zbl = {1092.11017},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1916/}
}
TY - JOUR
AU - Andreas Baltz
AU - Peter Hegarty
AU - Jonas Knape
AU - Urban Larsson
AU - Tomasz Schoen
TI - The structure of maximum subsets of \(\{1,\dots,n\}\) with no solutions to \(a+b=kc\)
JO - The electronic journal of combinatorics
PY - 2005
VL - 12
UR - http://geodesic.mathdoc.fr/articles/10.37236/1916/
DO - 10.37236/1916
ID - 10_37236_1916
ER -
%0 Journal Article
%A Andreas Baltz
%A Peter Hegarty
%A Jonas Knape
%A Urban Larsson
%A Tomasz Schoen
%T The structure of maximum subsets of \(\{1,\dots,n\}\) with no solutions to \(a+b=kc\)
%J The electronic journal of combinatorics
%D 2005
%V 12
%U http://geodesic.mathdoc.fr/articles/10.37236/1916/
%R 10.37236/1916
%F 10_37236_1916
Andreas Baltz; Peter Hegarty; Jonas Knape; Urban Larsson; Tomasz Schoen. The structure of maximum subsets of \(\{1,\dots,n\}\) with no solutions to \(a+b=kc\). The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1916
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