On Sumset Inequalities: A Mathematical Approach
Pathikrit Basu *
MSQE, Indian Statistical Institute, New Delhi, India and 20128 White Cloud Circle, West Linn, Oregon-97068, United States.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we study sumset inequalities concerning cardinalities of sumsets and functions of finite subsets of integers such as entropy and additive energy. We also identify sufficient conditions for existence of arithmetic progressions in difference sets and three-term progressions in differences of squares of prime numbers.
Keywords: Additive combinatorics, sumsets, entropy, additive energy