Samuel Korsky

activity

20192026

most citedOn the Computational Power of RNNs

19 citations · 19 across the 20 of their papers we have counts for

collaborators

21 papers

math.MG2026

Sharp Antipode-Neighbor Bounds in Every Dimension

Samuel Korsky

Let $P \subset R^{d}$ be finite with $diam (P) \leq 1$ . For $0 < ε < 1$ , let $N_{ε} (P)$ denote the number of ordered pairs at distance at most…

math.CO2026

A Resolution of the de Bruijn--Erdős Consecutive-Gap Problem

Samuel Korsky

Let $(x_{n})_{n \geq 1}$ be a sequence of distinct points on the unit circle. An $r$ -span is the total length of $r$ consecutive gaps determined by the inserted points. Write $M_n^{(r)…

math.NT2026

Affine Copies of Three-Point Patterns in Sets of Integers

Samuel Korsky

Let $P = {0, a, b}$ , where $0 < a < b$ and $g cd (a, b) = 1$ . For a finite set $A \subset Z$ , let $M_{P}^{+} (A)$ count the copies $x, x + a d, x + b d \in A$ with $d > 0$ , and let $M_{P} (A)$ count the…

math.NT2026

Improved Bounds for Distinct Multiples in Intervals

Kaizhe Chen, Samuel Korsky

For $n \geq 1$ , let $F (n)$ be the least $H$ such that any $H$ consecutive integers contain $n$ pairwise distinct integers $a_{1}, a_{2}, \dots, a_{n}$ with $k ∣ a_{k}$ for $1 \leq k \leq n$ , a…

math.NT2026

Positive Lower Density for Hofstadter's $ab - 1$ Problem

Samuel Korsky

Let $A$ be the smallest set of positive integers containing $2$ and $3$ such that $ab - 1 \in A$ whenever $a, b \in A$ are distinct. We prove that $A$ has positive lower density, answer…

math.CO2026

Long Lattice Paths with No Three Collinear Vertices

Samuel Korsky

For $d \geq 1$ , let $L (d) \in N \cup {\infty}$ be the supremum of the lengths of paths in $Z^{d}$ whose steps are standard basis vectors and whose vertex sets contain no…

math.CO2026

Asymptotically attaining the Moore bound

Wouter Cames van Batenburg, Samuel Korsky

For positive integers $d$ and $k$ , let $n_{k} (d)$ be the maximum order of a graph of maximum degree at most $d$ and diameter at most $k$ . We prove that $$ \lim_{d\to\infty}\frac{n_k(…

math.NT2026

Large Sets of Integers with No Harmonic Triples

Samuel Korsky

Let $f (N)$ denote the largest size of a set $A \subseteq [N] = {1, \dots, N}$ containing no distinct $a, b, c$ such that \[ \frac2a=\frac1b+\frac1c . \] We prove \[ f(N)\gg N\exp\!\lef…

math.NT2026

Approximating $1$ by Sums of Unit Fractions

Samuel Korsky

If a finite collection (with repetitions allowed) of unit fractions has sum larger than $K$ , how close can a sum of some of them come to $1$ from below? Improving a bound of Erdős…

math.CO2026

North-East Lattice Paths with Few Collinear Vertices

Samuel Korsky

Let $A (k)$ be the largest possible number of moves in a north-east lattice path whose visited vertices contain no $k$ collinear points. Gerver (1979) and Gerver and Ramsey (1979) g…

math.CO2026

Arithmetic Progression-Free Subset-Sum Sets

Samuel Korsky

For a finite set $A$ of positive integers, let $H (A)$ be its set of subset sums, including the empty sum, and let $g_{k} (n)$ be the least $N$ for which some $n$ -element set $A\subset…

math.CO2026

Hitting Arithmetic Progressions at the Square-Root Scale

Samuel Korsky

Let $f (N, k)$ be the minimum size of a subset of ${0, \dots, N - 1}$ meeting every $k$ -term arithmetic progression of positive difference contained in that interval. Improving on a b…

math.CO2026

An Improved Lower Bound for the de Bruijn--Erdős Consecutive Gap Problem

Samuel Korsky

Let $(x_{n})_{n \geq 1}$ be a sequence of distinct points on the unit circle. After the first $n$ points are inserted, the circle is divided into $n$ intervals. For a fixed integer $r…

math.NT2026

Inhomogeneous Approximation by Sums of Roots

Samuel Korsky

Let $d \geq 2$ and $k \geq 1$ be fixed. We prove that, for every $ε > 0$ and every real $β$ , there exist integers $1 \leq b_{1}, \dots, b_{k} \leq N$ such that \[ \left\|\sum_{j=1}^k b_j^{1/d…

math.CO2026

Lipschitz Functions on Sparse Graphs II

Samuel Korsky

Korsky, Saffat and Aiylam introduced a growth constant $c (G)$ for integer-valued $h$ -Lipschitz functions on a finite graph $G$ and proved that, for $G = G (n, d / n)$ , \[ \frac{1}{2d}+O(…

math.CO2026

Polylogarithmic Full-Chord Buffon Discrepancy

Samuel Korsky

Steinerberger introduced the Buffon discrepancy problem, asking how accurately a one-dimensional set of length $L$ in a convex body can match the Crofton-predicted line-intersectio…

math.CO2026

Randomly Shifted Steinhaus Longimeters and Buffon Discrepancy

Samuel Korsky

Let $Ω \subset R^{2}$ be a bounded convex domain. Steinerberger (2026) introduced the Buffon discrepancy problem: given length $L$ , construct a one-dimensional set $S\subsetΩ…

math.CO2026

Spectral Bounds for Antipodal Graphs

Samuel Korsky

Suppose ${x_{1}, \dots, x_{n}} \subset R^{2}$ is a set of $n$ points in the plane with diameter $\leq 1$ , meaning $∣ x_{i} - x_{j} ∣ \leq 1$ for all $1 \leq i, j \leq n$ .…

math.CO2024

Lipschitz Functions on Sparse Graphs

Samuel Korsky, Tahsin Saffat, Dhroova Aiylam

In this work we attempt to count the number of integer-valued $h$ -Lipschitz functions (functions that change by at most $h$ along edges) on two classes of sparse graphs; grid graph…

math.CO2021

Permutations of counters on a table

Samuel Korsky

We consider a game in which a blindfolded player attempts to set $n$ counters lying on the vertices of a rotating regular $n$ -gon table simultaneously to $0$ . When the counters cou…

cs.CL2019★ 19 cited

On the Computational Power of RNNs

Samuel A. Korsky, Robert C. Berwick

Recent neural network architectures such as the basic recurrent neural network (RNN) and Gated Recurrent Unit (GRU) have gained prominence as end-to-end learning architectures for…

Sharp Antipode-Neighbor Bounds in Every Dimension

A Resolution of the de Bruijn--Erdős Consecutive-Gap Problem

Affine Copies of Three-Point Patterns in Sets of Integers

Improved Bounds for Distinct Multiples in Intervals

Positive Lower Density for Hofstadter's ab−1 Problem

Long Lattice Paths with No Three Collinear Vertices

Asymptotically attaining the Moore bound

Large Sets of Integers with No Harmonic Triples

Approximating 1 by Sums of Unit Fractions

North-East Lattice Paths with Few Collinear Vertices

Arithmetic Progression-Free Subset-Sum Sets

Hitting Arithmetic Progressions at the Square-Root Scale

An Improved Lower Bound for the de Bruijn--Erdős Consecutive Gap Problem

Inhomogeneous Approximation by Sums of Roots

Lipschitz Functions on Sparse Graphs II

Polylogarithmic Full-Chord Buffon Discrepancy

Randomly Shifted Steinhaus Longimeters and Buffon Discrepancy

Spectral Bounds for Antipodal Graphs

Lipschitz Functions on Sparse Graphs

Permutations of counters on a table

On the Computational Power of RNNs

Positive Lower Density for Hofstadter's $ab - 1$ Problem

Approximating $1$ by Sums of Unit Fractions