Carl Schildkraut

activity

20242026

most citedSemi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems

3 citations · 4 across the 13 of their papers we have counts for

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9 papers · 1 filter

math.CO2026

A new lower bound for two-color van der Waerden numbers

Marcelo Campos, Jacob Fox, Carl Schildkraut

The van der Waerden number $w (k)$ is the smallest positive integer $N$ such that every two-coloring of ${1, 2, \dots, N}$ contains a monochromatic $k$ -term arithmetic progression.…

math.CO2026

On nearly consecutive sequences without long arithmetic progressions

Jacob Fox, Carl Schildkraut

A sequence $a_{1}, \dots, a_{n}$ of integers is nearly consecutive if $a_{i + 1} - a_{i} \in {1, 2}$ for $1 \leq i \leq n - 1$ . We prove that there are nearly consecutive sequences of length $…

math.CO2026

Dirac subgraphs of powers of cycles are Hamiltonian

Richard Lang, Alp Müyesser, Mathias Schacht +1

We show that, for every $ε > 0$ and all sufficiently large $k$ , any spanning subgraph of the $k$ th power of a cycle with minimum degree at least $(1 + ε) k$ contains…

math.CO2025

Abelian structure in approximate groups and Alon's conjecture on Ramsey Cayley graphs

Carl Schildkraut

A result of Pyber states that every finite group $G$ contains an abelian subgroup whose order is quasi-polynomially large in $∣ G ∣$ . We prove a similar result for $K$ -app…

math.CO2025

Words with Repeated Letters in a Grid

Zachary Halberstam, Carl Schildkraut

Given a word $w$ , what is the maximum possible number of appearances of $w$ reading contiguously along any of the directions in ${- 1, 0, 1}^{d} ∖ {0}$ in a large…

math.CO2025

Statistics of Erdős-Rényi random numerical semigroups

Noah Kravitz, Santiago Morales, Carl Schildkraut

For $p > 0$ a small parameter, let $A \subseteq Z_{> 0}$ be a random subset where each positive integer is included independently with probability $p$ . We show that,…

math.CO2025

Rainbow Trees in Hypercubes

Nicholas Crawford, Maya Sankar, Carl Schildkraut +1

We prove that every proper edge-coloring of the $n$ -dimensional hypercube $Q_{n}$ contains a rainbow copy of every tree $T$ on at most $n$ edges. This result is best possible, as $Q_…

math.CO2025

Expansion in Distance Matrices

John Byrne, Jacob Johnston, Carl Schildkraut +1

The normalized distance Laplacian matrix $D^{L} (G)$ of a graph $G$ is a natural generalization of the normalized Laplacian matrix, arising from the matrix of pa…

math.CO2024

More unit distances in arbitrary norms

Josef Greilhuber, Carl Schildkraut, Jonathan Tidor

For $d \geq 2$ and any norm on $R^{d}$ , we prove that there exists a set of $n$ points that spans at least $(\frac{d}{2} - o (1)) n lo g_{2} n$ unit distances under this norm for every…