William J. Wesley

activity

20222026

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3 papers · 1 filter

math.CO2022

Improved Ramsey-type theorems for Fibonacci numbers and other sequences

William J. Wesley

Van der Waerden's theorem states that for any positive integers $k$ and $r$ , there exists a smallest value $n = w (k, r)$ , called the van der Waerden number, such that every $r$ -colo…

math.CO2022

Rado Numbers and SAT Computations

Yuan Chang, Jesús A. De Loera, William J. Wesley

Given a linear equation $E$ , the $k$ -color Rado number $R_{k} (E)$ is the smallest integer $n$ such that every $k$ -coloring of ${1, 2, 3, \dots, n}$ contains a monoc…

math.CO2022

Ramsey Numbers through the Lenses of Polynomial Ideals and Nullstellensätze

Jesús A. De Loera, William J. Wesley

In this article we study the Ramsey numbers $R (r, s)$ through Hilbert's Nullstellensatz and Alon's Combinatorial Nullstellensatz. We give polynomial encodings whose solutions corres…