When Sets Can and Cannot Have MSTD Subsets

H Chu, N McNew, SJ Miller, V Xu, S Zhang - arxiv preprint arxiv …, 2016 - arxiv.org
A finite set of integers $ A $ is a sum-dominant (also called an More Sums Than Differences
or MSTD) set if $| A+ A|>| AA| $. While almost all subsets of $\{0,\dots, n\} $ are not sum …

Phase Transitions for Binomial Sets Under Linear Forms

R Jeong, SJ Miller - arxiv preprint arxiv:2309.01801, 2023 - arxiv.org
We generalize the study of the sum and difference sets of a subset of $\mathbb {N} $ drawn
from a binomial model to the following setting. Given $ A\subseteq\{0, 1,\dots, N\} $, an …

Distribution of missing differences in diffsets

S Harvey-Arnold, SJ Miller, F Peng - … Number Theory IV: CANT, New York …, 2021 - Springer
Abstract Lazarev, Miller and O'Bryant 11 investigated the distribution of| S+ S|| S+ S| for S
chosen uniformly at random from {0, 1,\dots, n-1\} 0, 1,⋯, n-1, and proved the existence of a …

When almost all sets are difference dominated in

A Hemmady, A Lott, SJ Miller - arxiv preprint arxiv:1608.03209, 2016 - arxiv.org
We investigate the behavior of the sum and difference sets of $ A\subseteq\mathbb
{Z}/n\mathbb {Z} $ chosen independently and randomly according to a binomial parameter …

Sum and Difference Sets in Generalized Dihedral Groups

R Ascoli, J Cheigh, R Jeong, A Keisling, A Lilly… - arxiv preprint arxiv …, 2022 - arxiv.org
Given a group $ G $, we say that a set $ A\subseteq G $ has more sums than differences
(MSTD) if $| A+ A|>| AA| $, has more differences than sums (MDTS) if $| A+ A|<| AA| $, or is …

Constructions of generalized MSTD sets in higher dimensions

E Kim, SJ Miller - Journal of Number Theory, 2022 - Elsevier
Text Let A be a set of finite integers, define A+ A={a 1+ a 2: a 1, a 2∈ A}, A− A={a 1− a 2: a 1,
a 2∈ A}, and for non-negative integers s and d define s A− d A= A+⋯+ A︸ s− A−⋯− A︸ d. A …

Distribution of Missing Differences in

S Harvey-Arnold, SJ Miller, F Peng - Combinatorial and Additive …, 2021 - books.google.com
Abstract Lazarev, Miller and O'Bryant [11] investigated the distribution of| S+ S| for S chosen
uniformly at random from {0, 1,..., n-1}, and proved the existence of a divot at missing 7 sums …

On the computational complexity of MSTD sets

T Mathur, TA Wong - arxiv preprint arxiv:1810.07358, 2018 - arxiv.org
We outline a general algorithm for verifying whether a subset of the integers is a more sum
than differences (MSTD) set, also known as sum dominated sets, and give estimates on its …

[PDF][PDF] Anand Hemmady1 Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts ash6@ williams. edu

A Lott, SJ Miller - INTEGERS, 2017 - math.colgate.edu
We investigate the behavior of the sum and difference sets of A⊆ Z/nZ chosen
independently and randomly according to a binomial parameter p (n)= o (1). We show that …

Problems in additive number theory, V: Affinely inequivalent MSTD sets

MB Nathanson - arxiv preprint arxiv:1609.01700, 2016 - arxiv.org
arxiv:1609.01700v3 [math.NT] 25 Jun 2017 Page 1 arxiv:1609.01700v3 [math.NT] 25 Jun
2017 PROBLEMS IN ADDITIVE NUMBER THEORY, V: AFFINELY INEQUIVALENT MSTD …