## 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

- MathematicsIntegers
- 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

- MathematicsExp. 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

- MathematicsIntegers
- 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.

## References

SHOWING 1-10 OF 22 REFERENCES

Some explicit constructions of sets with more sums than differences

- Mathematics
- 2007

We present a variety of new results on finite sets A of integers for which the sumset A+A is larger than the difference set A-A, so-called MSTD (more sums than differences) sets. First we show that…

Many sets have more sums than differences

- Mathematics
- 2006

Since addition is commutative but subtraction is not, the sumset S+S of a finite set S is predisposed to be smaller than the difference set S-S. In this paper, however, we show that each of the three…

When almost all sets are difference dominated

- MathematicsRandom Struct. Algorithms
- 2009

The heart of the approach involves using different tools to obtain strong concentration of the sizes of the sum and difference sets about their mean values, for various ranges of the parameter p, and exhibits a threshold phenomenon regarding the ratio of the size of the difference- to the sumset.

SETS WITH MORE SUMS THAN DIFFERENCES

- Mathematics
- 2006

Let A be a finite subset of the integers or, more generally, of any abelian group, written additively. The set A has more sums than di! erences if |A + A| > |A ! A|. A set with this property is…

Problems in additive number theory, I

- Mathematics
- 2006

Talk at the Atelier en combinatoire additive (Workshop on Arithmetic Combinatorics) at the Centre de recherches mathématiques at the Université de Montréal on April 8, 2006. Definition 1. A problem…

Problems in additive number theory, III

- Mathematics
- 2009

Let ℕ, ℕ0, ℤ and ℕ d denote, respectively, the sets of positive integers, non-negative integers, integers and d-dimensional integral lattice points. Let G denote an arbitrary abelian group and let X…

Constructing numerical semigroups of a given genus

- Mathematics
- 2010

Let ng denote the number of numerical semigroups of genus g. Bras-Amorós conjectured that ng possesses certain Fibonacci-like properties. Almost all previous attempts at proving this conjecture were…