Resistor network-based algorithms for enumerating rational numbers

  • Authors:

  • Samuel C. Hsieh;C. Van Nelson;Logeshbabu Sampath

  • Affiliations:

  • Ball State University, Muncie, Indiana;Ball State University, Muncie, Indiana;Ball State University, Muncie, Indiana

  • Venue:
  • Journal of Computing Sciences in Colleges
  • Year:
  • 2010

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Abstract

A class of simple resistor networks is used to enumerate the set of positive rational numbers. A one-to-one correspondence between the simple resistor networks and rational numbers is established, and efficient algorithms to find the rational for a given ordinal number, to find the ordinal number for a given rational, and to generate the rationals up to a given ordinal number are presented. The bijection and the algorithms answer some typical questions that are frequently asked by students in discrete mathematics or computing theory classes related to counting positive rational numbers.