Geodesic
Sidon Sets are Proportionally Sidon with Small Sidon Constants
Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 798-809

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/S0008439518000620
Mots-clés : Sidon set, independent set 
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
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[1] Bourgain, J., Propriétés de décomposition pour les ensembles de Sidon . Bull. Soc. Math. France 111(1983), 421–428. Google Scholar

[2] Bourgain, J., Subspaces of ℓ ∞ , arithmetical diameter and Sidon sets . In: Probability in Banach spaces V , Lecture Notes in Math., 1153, Springer, Berlin, 1985, pp. 96–127. Google Scholar | DOI

[3] Bourgain, J., Sidon sets and Riesz products . Ann. Inst. Fourier (Grenoble) 35(1985), 137–148. Google Scholar

[4] Graham, C. C. and Hare, K. E., Characterizing Sidon sets by interpolation properties of subsets . Colloq. Math. 112(2008), 175–199. Google Scholar | DOI

[5] Graham, C. C. and Hare, K. E., Interpolation and Sidon sets for compact groups , CMS Books in Math., Springer, New York, 2013. Google Scholar | DOI

[6] Grow, D., Sidon sets and I sets . Colloq. Math. 53(1987), 269–270. Google Scholar | DOI

[7] Hare, K. E. and Ramsey, L. T., The relationship between 𝜀-Kronecker and Sidon sets . Canad. Math. Bull. 59(2016), 521–527. Google Scholar | DOI

[8] Li, D. and Queffélec, H., Introduction à l’etude des espaces de Banach. Analyse et probabilités , Cours Spécalisés, 12, Société Mathématique de France, Paris, 2004. Google Scholar

[9] López, J. and Ross, K., Sidon sets , Lecture Notes in Pure and Applied Mathematics, 13, Marcel Dekker, New York, 1975. Google Scholar

[10] Malliavin-Brameret, M. P. and Malliavin, P., Caractérisation arithmétique des ensembles de Helson . C.R.Acad. Sci. Paris Sér. A–B 264(1967), A192–A193. Google Scholar

[11] Neuwirth, S., The maximum modulus of a trigonometric trinomial . J. Anal. Math. 104(2008), 371–396. Google Scholar | DOI

[12] Pisier, G., De nouvelles caractérisations des ensembles de Sidon . In: Mathematical analysis and applications, Part B , Adv. Math. Suppl. Studies, 7b, Academic Press, New York-London, 1981, pp. 685–726. Google Scholar

[13] Pisier, G., Conditions d’ entropie et caractérisations arithmétiques des ensembles de Sidon . Proc. Conf. on Modern Topics in Harmonic Analysis (Torino/Milano) . Ist. Naz. Alta Mat. Francesco Severi, Rome, 1983, pp. 911–944. Google Scholar

[14] Pisier, G., Arithmetic characterizations of Sidon sets . Bull. Amer. Math. Soc. 8(1983), 87–89. Google Scholar | DOI

[15] Ramsey, L. T., Comparisons of Sidon and I sets . Colloq. Math. 70(1996), 103–132. Google Scholar | DOI

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