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math.NT2015
Ramsey Theory Problems over the Integers: Avoiding Generalized Progressions
Andrew Best, Karen Huan, Nathan McNew +4
Two well studied Ramsey-theoretic problems consider subsets of the natural numbers which either contain no three elements in arithmetic progression, or in geometric progression. We…
math.NT2015
The emergence of 4-cycles in polynomial maps over the extended integers
Andrew Best, Patrick Dynes, Steven J. Miller +2
Let ; for each integer it is interesting to consider the number of iterates , if possible, needed to satisfy . The sets $\{α, f(α),…
math.NT2014
Geometric-progression-free sets over quadratic number fields
Andrew Best, Karen Huan, Nathan McNew +4
A problem of recent interest has been to study how large subsets of the natural numbers can be while avoiding 3-term geometric progressions. Building on recent progress on this pro…