11 citations · 17 across the 10 of their papers we have counts for
16 papers
Anti-concentration with respect to random permutations
Aaron Berger, Ross Berkowitz, Pat Devlin +1
Classical anti-concentration results focus on the random sum , where are independent random variables and are real numbers. In this paper, w…
Approximating Min-Diameter: Standard and Bichromatic
Aaron Berger, Jenny Kaufmann, Virginia Vassilevska Williams
The min-diameter of a directed graph is a measure of the largest distance between nodes. It is equal to the maximum min-distance across all pairs ,…
On sum-intersecting families of positive integers
Aaron Berger, Nitya Mani
We study the following natural arithmetic question regarding intersecting families: how large can a family of subsets of integers from be such that, for every pai…
Non-classical polynomials and the inverse theorem
Aaron Berger, Ashwin Sah, Mehtaab Sawhney +1
In this note we characterize when non-classical polynomials are necessary in the inverse theorem for the Gowers -norm. We give a brief deduction of the fact that a bounded fun…
-intersecting families of graphs
Aaron Berger, Yufei Zhao
Ellis, Filmus, and Friedgut proved an old conjecture of Simonovits and Sós showing that the maximum size of a triangle-intersecting family of graphs on vertices has size at mos…
Popular differences for matrix patterns
Aaron Berger, Ashwin Sah, Mehtaab Sawhney +1
The following combinatorial conjecture arises naturally from recent ergodic-theoretic work of Ackelsberg, Bergelson, and Best. Let , be integer matrices, …
Memoryless Worker-Task Assignment with Polylogarithmic Switching Cost
Aaron Berger, William Kuszmaul, Adam Polak +2
We study the basic problem of assigning memoryless workers to tasks with dynamically changing demands. Given a set of workers and a multiset of tasks,…
Popular Differences for Corners in Abelian Groups
Aaron Berger
For a compact abelian group , a corner in is a triple of points , , . The classical corners theorem of Ajtai and Szemerédi implies that for…
On Anti-Powers in Aperiodic Recurrent Words
Aaron Berger, Colin Defant
Fici, Restivo, Silva, and Zamboni define a $\textit{$k$-anti-power}$ to be a concatenation of consecutive words that are pairwise distinct and have the same length. They ask fo…
Connected-Intersecting Families of Graphs
Aaron Berger, Ross Berkowitz, Pat Devlin +4
For a graph property and a common vertex set , a family of graphs on is \emph{-intersecting} iff satisfies $\math…
Modified Erdös--Ginzburg--Ziv Constants for and
Aaron Berger, Danielle Wang
For an abelian group and an integer , the \emph{modified Erdös--Ginzburg--Ziv constant} is the smallest integer such that any zero-sum sequence of lengt…
On Gaps in the Closures of Images of Divisor Functions
Niven Achenjang, Aaron Berger
Given a complex number , define the divisor function by . In this paper, we look at , the top…
On the Distribution of Range for Tree-Indexed Random Walks
Aaron Berger, Caleb Ji, Erik Metz
We study tree-indexed random walks as introduced by Benjamini, Häggström, and Mossel, i.e. labelings of a tree for which adjacent vertices have labels differing by 1. It is a conje…
Progressions and Paths in Colorings of
Aaron Berger
A is a set such that any finite coloring of contains arbitrarily long monochromatic progressions with common difference in $…
An Analogue of the Erdős-Ginzburg-Ziv Theorem over
Aaron Berger
Let be a multiset of integers. We say is a if the sum of its elements is 0. We study zero-sum sequences whose elements lie in…
Query Complexity of Mastermind Variants
Aaron Berger, Christopher Chute, Matthew Stone
We study variants of Mastermind, a popular board game in which the objective is sequence reconstruction. In this two-player game, the so-called \textit{codemaker} constructs a hidd…