Pm numbers, ambiguity, and regularity

Abstract

We introduce the pseudo-m-ary (Pm) number system in which numbers are represented by sums of the form Zi>oai(mi+1=1). We characterize the Pm representations that are produced by the greedy algorithm and show that they form a regular set. In addition, we show that the set of Pm representations that are the sole representations for their corresponding numbers is also a regular set.