Dominance Over N

Abstract

Abstract.This paper provides an overview of the b-dominance order over the natural numbers, N, using the base b expansion of natural numbers. The b-dominance order is an accessible partially-ordered set that is less complex than the divisor relation but more complex than ≤; thus, it supplies a good medium through which an undergraduate can be exposed to the subject of order theory. Here we discuss many ideas in order theory, including the Poincaré polynomial and the Möbius function. Acknowledgements: The authors thank the M.J. Murdock Charitable Trust and the Pacific Lutheran University Division of Natural Sciences for their generous support. They would also like to extend their thanks to Dr. Tom Edgar for the project idea and all his help throughout their summer program. Page 24 RHIT Undergrad. Math. J., Vol. 14, no. 2