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    The number of partitions of a set and Superelliptic Diophantine equations

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    Name:
    AndricaBagdasarTurcas - Springer ...
    Embargo:
    2022-11-22
    Size:
    230.1Kb
    Format:
    PDF
    Description:
    Accepted Manuscript
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    Authors
    Andrica, Dorin
    Bagdasar, Ovidiu cc
    Ţurcaş, George Cătălin
    Affiliation
    “Babeş-Bolyai” University, Cluj-Napoca, Romania
    University of Derby
    The Institute of Mathematics of the Romanian Academy “Simion Stoilow” Bucharest, Romania
    Issue Date
    2020-11-22
    
    Metadata
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    Abstract
    In this chapter we start by presenting some key results concerning the number of ordered k-partitions of multisets with equal sums. For these we give generating functions, recurrences and numerical examples. The coefficients arising from these formulae are then linked to certain elliptic and superelliptic Diophantine equations, which are investigated using some methods from Algebraic Geometry and Number Theory, as well as specialized software tools and algorithms. In this process we are able to solve some recent open problems concerning the number of solutions for certain Diophantine equations and to formulate new conjectures.
    Citation
    Andrica D., Bagdasar O., and Ţurcaş G.C. (2020). ‘The number of partitions of a set and Superelliptic Diophantine equations’. In Raigorodskii A.M., and Rassias M.T. (Eds.). ‘Discrete Mathematics and Applications’. Switzerland: Springer, pp. 1-20.
    Publisher
    Springer
    URI
    http://hdl.handle.net/10545/625498
    DOI
    10.1007/978-3-030-55857-4_3
    Additional Links
    https://link.springer.com/chapter/10.1007/978-3-030-55857-4_3
    Type
    Book chapter
    Language
    en
    ISSN
    1931-6828
    EISSN
    1931-6836
    ISBN
    9783030558567
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-030-55857-4_3
    Scopus Count
    Collections
    Department of Electronics, Computing & Maths

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