New results and conjectures on 2-partitions of multisets

Conference paper

Bagdasar, O. and Andrica, D. 2017. New results and conjectures on 2-partitions of multisets. 7th International Conference on Modeling, Simulation, and Applied Optimization, ICMSAO 2017. IEEE Computer Society. https://doi.org/10.1109/icmsao.2017.7934928
AuthorsBagdasar, O. and Andrica, D.
TypeConference paper
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.

Keywordsinteger sequences and partitions; asymptotic formula ; unimodal sequence
Year2017
Conference7th International Conference on Modeling, Simulation, and Applied Optimization, ICMSAO 2017
PublisherIEEE Computer Society
Digital Object Identifier (DOI)https://doi.org/10.1109/icmsao.2017.7934928
Web address (URL)http://www.scopus.com/inward/record.url?eid=2-s2.0-85021414593&partnerID=MN8TOARS
https://ieeexplore.ieee.org/document/7934928
Journal citationpp. 1-5
Web address (URL) of conference proceedingshttps://ieeexplore.ieee.org/document/7934928
Output statusPublished
Publication dates29 May 2017
Publication process dates
Deposited05 Jun 2023
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Bagdasar, Ovidiu, Popovici, Nicolae and Bagdasar, O. 2017. LOCAL MAXIMIZERS OF GENERALIZED CONVEX VECTOR-VALUED FUNCTIONS. Journal of Nonlinear and Convex Analysis.
On the number of complex horadam sequences with a fixed period
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the number of complex horadam sequences with a fixed period. Fibonacci Quarterly.
On the characterization of periodic complex Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the characterization of periodic complex Horadam sequences. Fibonacci Quarterly.
On a result of Bunder involving Horadam sequences: A proof and generalization
Larcombe, Peter J. and Bagdasar, Ovidiu 2013. On a result of Bunder involving Horadam sequences: A proof and generalization. Fibonacci Quarterly.
Influence discovery in semantic networks: An initial approach
Trovati, M. and Bagdasar, O. 2014. Influence discovery in semantic networks: An initial approach. IEEE. https://doi.org/10.1109/uksim.2014.48
Complementary iInequalities involving the Stolarsky Mean
Bagdasar, Ovidiu 2010. Complementary iInequalities involving the Stolarsky Mean. Journal of Inequalities and Applications. https://doi.org/10.1155/2010/492570
Concise computer mathematics: tutorials on theory and problems
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/10.1080/10236198.2014.891022
Local 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/s11590-014-0781-3
A 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.2014.55
On 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-2019-0025
On 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
ON A RESULT OF BUNDER INVOLVING HORADAM SEQUENCES: A NEW PROOF
Larcombe, Peter J., Bagdasar, O. and Fennessey, Eric J. 2014. ON A RESULT OF BUNDER INVOLVING HORADAM SEQUENCES: A NEW PROOF. Fibonacci Quarterly. pp. 175-177.