Sidon Sets are Proportionally Sidon with Small Sidon Constants
Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 798-809
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In his seminal work on Sidon sets, Pisier found an important characterization of Sidonicity: A set is Sidon if and only if it is proportionally quasi-independent. Later, it was shown that Sidon sets were proportionally “special” Sidon in several other ways. Here, we prove that Sidon sets in torsion-free groups are proportionally $n$-degree independent, a higher order of independence than quasi-independence, and we use this to prove that Sidon sets are proportionally Sidon with Sidon constants arbitrarily close to one, the minimum possible value.
Hare, Kathryn E.; Yang, Robert (Xu). Sidon Sets are Proportionally Sidon with Small Sidon Constants. Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 798-809. doi: 10.4153/S0008439518000620
@article{10_4153_S0008439518000620,
author = {Hare, Kathryn E. and Yang, Robert (Xu)},
title = {Sidon {Sets} are {Proportionally} {Sidon} with {Small} {Sidon} {Constants}},
journal = {Canadian mathematical bulletin},
pages = {798--809},
year = {2019},
volume = {62},
number = {4},
doi = {10.4153/S0008439518000620},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000620/}
}
TY - JOUR AU - Hare, Kathryn E. AU - Yang, Robert (Xu) TI - Sidon Sets are Proportionally Sidon with Small Sidon Constants JO - Canadian mathematical bulletin PY - 2019 SP - 798 EP - 809 VL - 62 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000620/ DO - 10.4153/S0008439518000620 ID - 10_4153_S0008439518000620 ER -
%0 Journal Article %A Hare, Kathryn E. %A Yang, Robert (Xu) %T Sidon Sets are Proportionally Sidon with Small Sidon Constants %J Canadian mathematical bulletin %D 2019 %P 798-809 %V 62 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008439518000620/ %R 10.4153/S0008439518000620 %F 10_4153_S0008439518000620
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