Tree Structures on Partitions Shaped by the Dynamics of the Triangle Map by Joe Fox '24

Tree Structures on Partitions Shaped by the Dynamics of the Triangle Map by Joe Fox ’24, Monday May 13, 1:45 – 2:30pm, North Science Building 015, Wachenheim, Mathematics Thesis

We use the slow triangle map (a type of multi-dimensional continued fraction algorithm) to construct a tree structure displaying all integer partitions of a positive integer $n$. We then link these tree structures to the underlying dynamics of the triangle map by visualizing the natural extension. Finally, we discuss the natural extensions and dynamics of other partition-friendly algorithms.