This paper provides an overview of the b-dominance order over the natural numbers, ℵ, 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 Poincare polynomial and the Mobius function.
Prof. Tom Edgar, Assistant Professor or Mathematics, Pacific Lutheran University
Ball, Tyler and Juda, Daniel
"Dominance Over ℵ,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 14
, Article 2.
Available at: http://scholar.rose-hulman.edu/rhumj/vol14/iss2/2