Samuel Korsky

collaborators

14 papers

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

A Stretched-Exponential Bound for an Erdos--Graham Unit-Fraction Problem

Samuel Korsky

For a finite multiset $A$ of positive integers, write $R (A) = \sum_{a \in A} a^{- 1}$ and let $ε (A)$ be the distance from $1$ to the largest reciprocal subsum of $A$ …

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 $1 \leq i, j \leq n$ .…

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

A Stretched-Exponential Bound for an Erdos--Graham Unit-Fraction Problem

Spectral Bounds for Antipodal Graphs

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