Geodesic
On modular \(k\)-free sets
Victor Lambert1
1Ecole Polytechnique
The electronic journal of combinatorics, Tome 22 (2015) no. 2
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Let $n$ and $k$ be integers. A set $A\subset\mathbb{Z}/n\mathbb{Z}$ is $k$-free if for all $x$ in $A$, $kx\notin A$. We determine the maximal cardinality of such a set when $k$ and $n$ are coprime. We also study several particular cases and we propose an efficient algorithm for solving the general case. We finally give the asymptotic behaviour of the minimal size of a $k$-free set in $\left[ 1,n\right]$ which is maximal for inclusion.
DOI : 10.37236/4704
Classification : 05D05, 11B75, 11P99
Mots-clés : Sidon sets, congruence, algorithm, additive number theory

Victor Lambert  1

1 Ecole Polytechnique 
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     author = {Victor Lambert},
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     journal = {The electronic journal of combinatorics},
     year = {2015},
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     number = {2},
     doi = {10.37236/4704},
     zbl = {1312.05136},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4704/}
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Victor Lambert. On modular \(k\)-free sets. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/4704

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