Two mechanisms for generating infinite families of pairing bijections

Authors:
Paul Tarau
Affiliations:
University of North Texas
Venue:
Proceedings of the 2013 Research in Adaptive and Convergent Systems
Year:
2013

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Abstract

We explore two general mechanisms for producing pairing bijections (bijective functions defined from N2 → N). The first mechanism, using n-adic valuations results in parameterized algorithms generating a countable family of distinct pairing bijections. The second mechanism, using characteristic functions of subsets of N provides 2N distinct pairing bijections. Mechanisms to combine such pairing bijections and their application to generate families of permutations of N are also described. The paper uses a small subset of the functional language Haskell to provide executable specifications of various the functions defined in a literate programming style.