Sumset Bound |A+B| ≥ |A|+|B|-1 in Additive Combinatorics

Explanations 2

• Recall that A+BA+BA+B denotes the set of all real numbers a+ba+ba+b for aaa in AAA and bbb in BBB. Let ∣A∣=m|A|=m∣A∣=m, and ∣B∣=n|B|=n∣B∣=n where mmm and nnn are positive intege…

  By Ryan Alweiss, Victor Wang, Samuel Hsiang

• (2009 USAMO #2) Let nnn be a positive integer. Determine the size of the largest subset of {−n,−n+1,…,n−1,n}\{-n, -n+1, \ldots , n-1, n\}{−n,−n+1,…,n−1,n} which does not contain…

  By Franklyn Wang