The number of partitions of a set and Superelliptic Diophantine equations
Book chapter
Andrica, Dorin, Bagdasar, Ovidiu and Ţurcaş, George Cătălin 2020. The number of partitions of a set and Superelliptic Diophantine equations. in: Springer Optimization and Its Applications Springer.
| Authors | Andrica, Dorin, Bagdasar, Ovidiu and Ţurcaş, George Cătălin |
|---|---|
| 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 |
| Year | 2020 |
| Book title | Springer Optimization and Its Applications |
| Discrete Mathematics and Applications | |
| Publisher | Springer |
| ISBN | 9783030558567 |
| ISSN | 1931-6828 |
| 1931-6836 | |
| Digital Object Identifier (DOI) | https://doi.org/10.1007/978-3-030-55857-4_3 |
| Web address (URL) | http://hdl.handle.net/10545/625498 |
| http://www.springer.com/tdm | |
| hdl:10545/625498 | |
| File | |
| File | File Access Level Open |
| Publication dates | 22 Nov 2020 |
| Publication process dates | |
| Deposited | 05 Jan 2021, 11:06 |
| Accepted | Jul 2020 |
| Contributors | “Babeş-Bolyai” University, Cluj-Napoca, Romania, University of Derby and The Institute of Mathematics of the Romanian Academy “Simion Stoilow” Bucharest, Romania |
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Bagdasar, Ovidiu and Larcombe, Peter J. 2014. On the characterization of periodic generalized Horadam sequences. Journal of Difference Equations and Applications. https://doi.org/10.1080/10236198.2014.891022Local maximum points of explicitly quasiconvex functions
Bagdasar, Ovidiu and Popovici, Nicolae 2014. Local maximum points of explicitly quasiconvex functions. Optimization Letters. https://doi.org/10.1007/s11590-014-0781-3A horadam-based pseudo-random number generator
Bagdasar, O.D., Chen, M. and Bagdasar, O. 2014. A horadam-based pseudo-random number generator. IEEE. https://doi.org/10.1109/uksim.2014.55On the structure of periodic complex Horadam orbits
Bagdasar, Ovidiu D., Larcombe, Peter J., Anjum, Ashiq and Bagdasar, O. 2016. On the structure of periodic complex Horadam orbits. Carpathian Journal of Mathematics.Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems
Popa, I.-L., Ceauşu, T., Bagdasar, O. and Agarwal, R.P. 2016. Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. 27 (2), pp. 153-166. https://doi.org/10.2478/auom-2019-0025On some functions involving the lcm and gcd of integer tuples
Bagdasar, Ovidiu 2014. On some functions involving the lcm and gcd of integer tuples. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics. https://doi.org/10.5937/SPSUNP1402091B