00:00:00 / 00:00:00

$k$-sum free sets in $[0,1]$

By Anne de Roton

Appears in collections : Additive combinatorics in Marseille / Combinatoire additive à Marseille, Exposés de recherche

Let $k > 2$ be a real number. We inquire into the following question : what is the maximal size (inner Lebesque measure) and the form of a set avoiding solutions to the linear equation $x + y = kz$ ? This problem was used for $k$ an integer larger than 4 to guess the density and the form of a corresponding maximal set of positive integers less than $N$. Nevertheless, in the case $k = 3$, the discrete and the continuous setting happen to be very different. Although the structure of maximal sets in the continuous setting is quite easy to describe for $k$ far enough from 2, it is more difficult to handle as $k$ comes closer to 2. Joint work with Alain Plagne.

Information about the video

Citation data

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback