8 citations · 16 across the 5 of their papers we have counts for
7 papers
The Erdős--Sós Conjecture: A visual exposition of the proof discovered by GPT-6 Astra
Jay Cummings
The Erdős--Sós theorem states that every graph of average degree greater than contains every tree on vertices. A short counting proof was discovered by GPT-6 Astra in 202…
A New Lower Bound for van der Waerden Numbers
Thomas Blankenship, Jay Cummings, Vladislav Taranchuk
In this paper we prove a new recurrence relation on the van der Waerden numbers, . In particular, if is a prime and then $w(r, k) > p \cdot \left(w\left(r - \…
A forest building process on simple graphs
Zhanar Berikkyzy, Steve Butler, Jay Cummings +4
Consider the following process on a simple graph without isolated vertices: Order the edges randomly and keep an edge if and only if it contains a vertex which is not contained in…
On the distance spectra of graphs
Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy +8
The distance matrix of a graph is the matrix containing the pairwise distances between vertices. The distance eigenvalues of are the eigenvalues of its distance matrix and…
Juggling card sequences
Steve Butler, Fan Chung, Jay Cummings +1
Juggling patterns can be described by a sequence of cards which keep track of the relative order of the balls at each step. This interpretation has many algebraic and combinatorial…
An Anti-Ramsey Problem Concerning Complete Bipartite Graphs
Stephan Cho, Jay Cummings, Colin Defant +1
We consider quadruples of positive integers with and such that any proper edge-coloring of the complete bipartite graph contains a rainbow…