Some remarks on 3-partitions of multisets.

Journal article

Andrica, Dorin and Bagdasar, Ovidiu 2018. Some remarks on 3-partitions of multisets. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.11.001
AuthorsAndrica, Dorin and Bagdasar, Ovidiu
Abstract

Partitions play an important role in numerous combinatorial optimization problems. Here we introduce the number of ordered 3-partitions of a multiset M having equal sums denoted by S(m1, ..., mn; α1, ..., αn), for which we find the generating function and give a useful integral formula. Some recurrence formulae are then established and new integer sequences are added to OEIS, which are related to the number of solutions for the 3-signum equation.

Partitions play an important role in numerous combinatorial optimization problems.
Here we introduce the number of ordered 3-partitions of a multiset M having equal
sums denoted by S(m1, ..., mn; α1, ..., αn), for which we find the generating function
and give a useful integral formula. Some recurrence formulae are then established
and new integer sequences are added to OEIS, which are related to the number of
solutions for the 3-signum equation.

KeywordsMultiset; 3-partition of a multiset; Generating function; Asymptotic formula; 3-signum equation
Year2018
JournalElectronic Notes in Discrete Mathematics
PublisherElsevier
ISSN1571-0653
Digital Object Identifier (DOI)https://doi.org/10.1016/j.endm.2018.11.001
Web address (URL)http://hdl.handle.net/10545/623231
http://creativecommons.org/licenses/by/4.0/
hdl:10545/623231
Publication dates06 Dec 2018
Publication process dates
Deposited17 Dec 2018, 14:15
SeriesProceedings of TCDM'2018
ContributorsBabeş-Bolyai University and University of Derby
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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.