Mathematics Colloquia and Seminars

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Van der Waerden's Theorem states that for any positive
integers k and r, there exists some number n such that if each integer
from 1 to n is assigned one of r colors, there exists a k-term
arithmetic progression whose elements are all the same color. The
problem of computing the smallest such n is difficult, and few values
are known. We will discuss several natural modifications of this problem
and the computational approaches to solve them. In particular, we
investigate the Ramsey-theoretic properties of the Fibonacci numbers and
related combinatorial words.