New results and conjectures on 2-partitions of multisets.
Journal article
Bagdasar, Ovidiu and Andrica, Dorin 2017. New results and conjectures on 2-partitions of multisets. Proceedings of the 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO). https://doi.org/10.1109/ICMSAO.2017.7934928
| Authors | Bagdasar, Ovidiu and Andrica, Dorin |
|---|---|
| Abstract | The interplay between integer sequences and partitions has led to numerous interesting results, with implications in generating functions, integral formulae, or combinatorics. An illustrative example is the number of solutions at level n to the signum equation. Denoted by S(n), this represents the number of ways of choosing + and - such that ±1±2±3±···±n = 0 (see A063865 in OEIS). The Andrica-Tomescu conjecture regarding the asymptotic behaviour of S(n) was solved affirmatively in 2013, and new conjectures were formulated since then. In this paper we present recurrence formulae, generating functions and integral formulae for the number of ordered 2-partitions of the multiset M having equal sums. Certain related integer sequences not currently indexed in the OEIS are then presented. Finally, we formulate conjectures regarding the unimodality, distribution and asymptotic behaviour of these sequences. |
| Keywords | Combinatorial mathematics; Integer programming; Generating functions; Recurrence formulae; Integral formulae; Integer sequences; Asymptotic formula |
| Year | 2017 |
| Journal | Proceedings of the 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO) |
| Publisher | Institute of Electrical and Electronic Engineers |
| Digital Object Identifier (DOI) | https://doi.org/10.1109/ICMSAO.2017.7934928 |
| Web address (URL) | http://hdl.handle.net/10545/622402 |
| http://creativecommons.org/licenses/by-nc-sa/4.0/ | |
| hdl:10545/622402 | |
| Publication dates | Apr 2017 |
| Publication process dates | |
| Deposited | 21 Mar 2018, 11:38 |
| ISBN | 9781509054541 |
| Contributors | University of Derby and Babes¸-Bolyai University |
| File | |
| File | File Access Level Open |
| File | File Access Level Open |
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Bagdasar, Ovidiu 2013. Concise computer mathematics: tutorials on theory and problems. Springer.On the characterization of periodic generalized Horadam sequences
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