Aaron Robertson

Refined Restricted Permutations

Abstract. Define

On the asymptotic minimum number of monochromatic 3-term arithmetic progressions

S_{k}^n (\alpha)

Refined restricted involutions

to be the set of permutations of {1, 2,...,n} with exactly k fixed points which avoid the pattern

On generalized van der Waerden triples

\alpha\in S_m

Van der Waerden's Theorem and Avoidability in Words

. Let

Avoiding Monochromatic Sequences With Special Gaps

S_{k}^n (\alpha)

A probabilistic threshold for monochromatic arithmetic progressions

be the size of

Van der Waerden’s theorem

S_{k}^n (\alpha)

Ramsey Theory on the Integers

. We investigate

Permutation Patterns and Continued Fractions

S_{n}^0 (\alpha)