# Sets characterized by missing sums and differences

@article{Zhao2011SetsCB,
title={Sets characterized by missing sums and differences},
author={Yufei Zhao},
journal={Journal of Number Theory},
year={2011},
volume={131},
pages={2107-2134}
}
• Yufei Zhao
• Published 12 November 2009
• Mathematics
• Journal of Number Theory
38 Citations
S ep 2 01 7 A GEOMETRIC PERSPECTIVE ON THE MSTD QUESTION
• Mathematics
• 2018
A more sums than differences (MSTD) set A is a subset of Z for which |A + A| > |A − A|. Martin and O’Bryant used probabilistic techniques to prove that a non-vanishing proportion of subsets of {1, .
Explicit Constructions of Large Families of Generalized More Sums Than Differences Sets
• Mathematics
Integers
• 2012
In the course of constructing a large family of sets A, it is found that for any integer k there is an A such that, and it is shown that the minimum span of such a set is 30.
#A60 INTEGERS 19 (2019) INFINITE FAMILIES OF PARTITIONS INTO MSTD SUBSETS
• Mathematics
• 2019
A set A is MSTD (more-sum-than-di↵erence) if |A + A| > |A A|. Though MSTD sets are rare, Martin and O’Bryant proved that there exists a positive constant lower bound for the proportion of MSTD
Distribution of Missing Sums in Sumsets
• Mathematics
Exp. Math.
• 2013
Zhao proved that the limits exist, and that ∑ k⩾0 m(k)=1 and an explicit formula for the variance of |A+A| in terms of Fibonacci numbers is derived, finding that .
Generalizations of a Curious Family of MSTD Sets Hidden By Interior Blocks
• Mathematics
• 2018
A set $A$ is MSTD (more-sum-than-difference) or sum-dominant if $|A+A|>|A-A|$ and is RSD (restricted-sum dominant) if $|A\hat{+}A|>|A-A|$, where $A\hat{+}A$ is the sumset of $A$ without a number
Most Subsets Are Balanced in Finite Groups
• Mathematics
• 2014
The sumset is one of the most basic and central objects in additive number theory. Many of the most important problems (such as Goldbach’s conjecture and Fermat’s last theorem) can be formulated in
On Sets with More Restricted Sums than Differences
• Mathematics
Integers
• 2013
Though intuition suggests that such sets should be rare, it is proved that a positive proportion of subsets of {0, 1, . . . n−1} are restricted-sum-dominant sets.