Geodesic
Extremal subsets of \(\{1,\dots ,n\}\) avoiding solutions to linear equations in three variables
The electronic journal of combinatorics, Tome 14 (2007)

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Zbl arXiv EuDML
We refine previous results to provide examples, and in some cases precise classifications, of extremal subsets of $\{1,...,n\}$ containing no solutions to a wide class of non-invariant, homogeneous linear equations in three variables, i.e.: equations of the form $ax+by=cz$ with $a+b \neq c$.
DOI : 10.37236/992
Classification : 05D05, 11P99, 11B75 
Peter Hegarty. Extremal subsets of \(\{1,\dots ,n\}\) avoiding solutions to linear equations in three variables. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/992
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     author = {Peter Hegarty},
     title = {Extremal subsets of \(\{1,\dots ,n\}\) avoiding solutions to linear equations in three variables},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/992},
     zbl = {1157.05335},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/992/}
}
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