Graphical Composition

A partition can be thought of as a classification system, which sorts things into classes. The most basic example of this in mathematics is counting, which sorts collections into classes according to the number of things in the collection, so that for example any collection of ten things would be sorted into the same class.

More abstract uses of partitions, and similar constructions are common throughout mathematics. My proposed research aims to gain a deeper understanding of Graphical composition, which is an operation which combines the information from multiple partitions to give a single partition. An analogy for this would be examining two photographs of the same object, taken from different angles, to understand the three-dimensional structure of the object. Combining the information from multiple partitions can be a surprisingly complicated issue. A deeper understanding of how this can be done has the potential to impact a large number of fields of mathematical research, particularly algebra. There are also potential applications to other fields, such as statistical genetics.