The Number of Partitions of a Set and Superelliptic Diophantine Equations

Dorin Andrica (), Ovidiu Bagdasar () and George Cătălin Ţurcaş ()
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Dorin Andrica: “Babeş-Bolyai” University
Ovidiu Bagdasar: University of Derby
George Cătălin Ţurcaş: “Babeş-Bolyai” University

A chapter in Discrete Mathematics and Applications, 2020, pp 35-55 from Springer

Abstract: 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.

Keywords: Multiset; Partitions of a multiset; Elliptic curves; Hyperelliptic curves; Primary 14G05, 05A18; Secondary 11P81, 11Y50 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-55857-4_3

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DOI: 10.1007/978-3-030-55857-4_3

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