Department of

January 2021 February 2021 March 2021 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 1 2 3 4 5 6 1 2 3 4 5 6 3 4 5 6 7 8 9 7 8 9 10 11 12 13 7 8 9 10 11 12 13 10 11 12 13 14 15 16 14 15 16 17 18 19 20 14 15 16 17 18 19 20 17 18 19 20 21 22 23 21 22 23 24 25 26 27 21 22 23 24 25 26 27 24 25 26 27 28 29 30 28 28 29 30 31 31

Friday, February 12, 2021

**Abstract:** An old conjecture in additive combinatorics asks: what is the largest sum-free subset of any set of N positive integers? Here the word "largest" should be understood in terms of cardinality. For example, the largest sum-free subset of the first N positive integers has cardinality [(N+1)/2], which is the number of odd integers smaller than N, as well as the number of integers that lie in the interval [N/2,N]. In this talk, I will discuss a special case of the sum-free conjecture and the analogous conjecture on (k,l)-sum-free sets. This is a joint work with Yifan Jing