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The Number of Partitions of a Set and Superelliptic Diophantine Equations

In: Discrete Mathematics and Applications

Author

Listed:
  • Dorin Andrica

    (“Babeş-Bolyai” University)

  • Ovidiu Bagdasar

    (University of Derby)

  • George Cătălin Ţurcaş

    (“Babeş-Bolyai” University
    The Institute of Mathematics of the Romanian Academy “Simion Stoilow”)

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.

Suggested Citation

  • Dorin Andrica & Ovidiu Bagdasar & George Cătălin Ţurcaş, 2020. "The Number of Partitions of a Set and Superelliptic Diophantine Equations," Springer Optimization and Its Applications, in: Andrei M. Raigorodskii & Michael Th. Rassias (ed.), Discrete Mathematics and Applications, pages 35-55, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-55857-4_3
    DOI: 10.1007/978-3-030-55857-4_3
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