Dogs Probably Use the Factorial Base to do Math by Joanne Beckford ’19, Mathematics Colloquium, Wednesday, April 17, 1 – 1:45 pm, Stetson Court Classroom 101
Abstract: Humans, in particular, like to use base 10, however, every non-negative integer can be written using what is known as the factorial base representation. This notion will be defined and certain combinatorial structures arising from the arithmetic of these representations explored. In particular, I will investigate the sum-of-digits function, carry sequences, and a partial order referred to as digital dominance. Finally, I’ll describe an analog of a classical theorem due to Kummer that relates the combinatorial objects of interest by constructing a variety of new integer sequences.