Akshunna Shaurya Dogra, New York University (NYU)

Abstract

This talk will discuss minimal length representations of the Natural numbers under elements from a pre-defined symbol library O. We will mostly focus on symbol libraries consisting of 1 and different kinds of hyper-operations. We will go over both general and specific patterns emerging from different choices of symbol libraries, obtain bounds on the lengths expected, define numbers of special interest and prove and/or experimentally verify the existence of certain behaviors in these numbers. If time permits, we will also discuss how the results obtained can be generalized to a discussion on discrete posets, explore connections to monoid theory and prove/predict number theoretic results from the machinery discussed in the talk.