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Experimental Mathematics Seminar

Minimal length representations of the natural numbers and why they matter 

Akshunna Shaurya Dogra - Rutgers University

Location:  Hill 705
Date & time: Thursday, 11 October 2018 at 5:00PM - 5:48PM

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.