We study novel arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects.

For numbers corresponding to Catalan objects of low structural complexity our algorithms provide super-exponential gains while their average case complexity is within constant factors of their traditional counterparts.


hereditary numbering systems arithmetic algorithms for Combinatorial objects structural complexity of natural numbers run-length compressed numbers Catalan families 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Paul Tarau
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of North TexasUSA

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