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Emulating Primality with Multiset Representations of Natural Numbers

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Book cover Theoretical Aspects of Computing – ICTAC 2011 (ICTAC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6916))

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Abstract

Factorization results in multisets of primes and this mapping can be turned into a bijection between multisets of natural numbers and natural numbers. At the same time, simpler and more efficient bijections exist that share some interesting properties with the bijection derived from factorization.

This paper describes mechanisms to emulate properties of prime numbers through isomorphisms connecting them to computationally simpler representations involving bijections from natural numbers to multisets of natural numbers.

As a result, interesting automorphisms of ℕ and emulations of the rad, Möbius and Mertens functions emerge in the world of our much simpler multiset representations.

The paper is organized as a self-contained literate Haskell program. The code extracted from the paper is available as a standalone program at http://logic.cse.unt.edu/tarau/research/2011/mprimes.hs .

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of North Texas, Denton, Texas

    Paul Tarau

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  1. Paul Tarau
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Editor information

Editors and Affiliations

  1. International Institute for Software Technology, The United Nations University, Casa Silva Mendes, Est. do Engenheiro Trigo No. 4, Macau, China

    Antonio Cerone

  2. Data Abstraction (Pty) Ltd, 7 Saint David’s Park, Saint David’s Place, Parktown, Johannesburg, South Africa

    Pekka Pihlajasaari

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Tarau, P. (2011). Emulating Primality with Multiset Representations of Natural Numbers. In: Cerone, A., Pihlajasaari, P. (eds) Theoretical Aspects of Computing – ICTAC 2011. ICTAC 2011. Lecture Notes in Computer Science, vol 6916. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23283-1_15

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  • DOI: https://doi.org/10.1007/978-3-642-23283-1_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23282-4

  • Online ISBN: 978-3-642-23283-1

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