A simple bijection between σ and n ⌣{0}

Abstract

A simple bijection has been developed between Σ^∗ and N ⌣{0} from the considerations of the m-ary number systems and lexicographic ordering of strings where Σ is a finite alphabet set of size m. The simple proof of bijectivity leads to efficient algorithms for ranking and unranking of elements of Σ^∗.

Keywords:

• Bijection
• enumeration of strings
• theory of computation
• unranking of strings