3 citations · 4 across the 13 of their papers we have counts for
14 papers
Forcible groups and Frattini covers
Sean Eberhard, Robert M. Guralnick, Carl Schildkraut +1
We say that a finite group *forces* a finite group if every finite cover of contains a subgroup isomorphic to , and we say is *forcible* if some finite group …
A new lower bound for two-color van der Waerden numbers
Marcelo Campos, Jacob Fox, Carl Schildkraut
The van der Waerden number is the smallest positive integer such that every two-coloring of contains a monochromatic -term arithmetic progression.…
On nearly consecutive sequences without long arithmetic progressions
Jacob Fox, Carl Schildkraut
A sequence of integers is nearly consecutive if for . We prove that there are nearly consecutive sequences of length $…
More sum-product type counterexamples: products with shifts and
Oliver Roche-Newton, Carl Schildkraut, Audie Warren
Adapting the construction disproving the sum-product conjecture over present in Bloom, Sawin, Schildkraut and Zhelezov, we show the existence of a constant and ar…
Dirac subgraphs of powers of cycles are Hamiltonian
Richard Lang, Alp Müyesser, Mathias Schacht +1
We show that, for every and all sufficiently large , any spanning subgraph of the th power of a cycle with minimum degree at least contains…
The sum-product conjecture is false for real numbers
Thomas F Bloom, Will Sawin, Carl Schildkraut +1
We disprove the sum-product conjecture for real numbers by constructing arbitrarily large (whose elements are algebraic integers in a number field of degree $…
Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems
Tony Feng, Trieu Trinh, Garrett Bingham +21
We present a case study in semi-autonomous mathematics discovery, using Gemini to systematically evaluate 700 conjectures labeled 'Open' in Bloom's Erdős Problems database. We empl…
Abelian structure in approximate groups and Alon's conjecture on Ramsey Cayley graphs
Carl Schildkraut
A result of Pyber states that every finite group contains an abelian subgroup whose order is quasi-polynomially large in . We prove a similar result for -app…
Words with Repeated Letters in a Grid
Zachary Halberstam, Carl Schildkraut
Given a word , what is the maximum possible number of appearances of reading contiguously along any of the directions in in a large…
Statistics of Erdős-Rényi random numerical semigroups
Noah Kravitz, Santiago Morales, Carl Schildkraut
For a small parameter, let be a random subset where each positive integer is included independently with probability . We show that,…
Rainbow Trees in Hypercubes
Nicholas Crawford, Maya Sankar, Carl Schildkraut +1
We prove that every proper edge-coloring of the -dimensional hypercube contains a rainbow copy of every tree on at most edges. This result is best possible, as $Q_…
Expansion in Distance Matrices
John Byrne, Jacob Johnston, Carl Schildkraut +1
The normalized distance Laplacian matrix of a graph is a natural generalization of the normalized Laplacian matrix, arising from the matrix of pa…
More unit distances in arbitrary norms
Josef Greilhuber, Carl Schildkraut, Jonathan Tidor
For and any norm on , we prove that there exists a set of points that spans at least unit distances under this norm for every…
Lower bounds for sphere packing in arbitrary norms
Carl Schildkraut
We show that in any -dimensional real normed space, unit balls can be packed with density at least \[\frac{(1-o(1))d\log d}{2^{d+1}},\] improving a result of Schmidt from 1958 b…