Ensembles de petite somme, structure de sous-criticité
Robin Riblet1
1 26 rue du Caire 75002 Paris, France
Journal de théorie des nombres de Bordeaux, Volume 35 (2023) no. 3, pp. 697-749.

In 1991, Ruzsa proved a precise lower bound for the measure of the sum of two bounded sets of real numbers A and B involving the ratio λ(A)/λ(B) and the diameter of B. The structure of critical sets for this lower bound was described by Roton in 2018. In this paper, we describe the structure of nearly critical sets for Ruzsa’s inequality.

En 1991, Ruzsa a démontré une minoration précise de la mesure de la somme de deux ensembles bornés de réels A et B faisant intervenir le ratio λ(A)/λ(B) et le diamètre de B. La structure des ensembles critiques pour cette minoration a été décrite par Roton en 2018. Dans cet article, nous décrivons la structure des ensembles presque critiques pour l’inégalité de Ruzsa.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1261
Classification: 28A75, 11B13, 05B10
Keywords: Combinatoire additive, somme de Minkowski, structure, mesure d’ensembles, problème inverse, ensembles critiques, sumsets

Robin Riblet 1

1 26 rue du Caire 75002 Paris, France
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Robin Riblet. Ensembles de petite somme, structure de sous-criticité. Journal de théorie des nombres de Bordeaux, Volume 35 (2023) no. 3, pp. 697-749. doi : 10.5802/jtnb.1261. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1261/

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