Geodesic
Permutations avoiding arithmetic patterns
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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A permutation $\pi$ of an abelian group $G$ (that is, a bijection from $G$ to itself) will be said to avoid arithmetic progressions if there does not exist any triple $(a,b,c)$ of elements of $G$, not all equal, such that $c-b=b-a$ and $\pi(c)-\pi(b)=\pi(b)- \pi(a)$. The basic question is, which abelian groups possess such a permutation? This and problems of a similar nature will be considered.
DOI : 10.37236/1792
Classification : 11B25, 05A05, 20K99
Mots-clés : Pattern avoiding permutations, arithmetic progressions, Sidon sets 
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     author = {Peter Hegarty},
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Peter Hegarty. Permutations avoiding arithmetic patterns. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1792

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