On some results concerning the polygonal polynomials
Journal article
Andrica, D. and Bagdasar, O. 2019. On some results concerning the polygonal polynomials. Carpathian Journal of Mathematics. Vol 35 (Issue 1), pp. 1-12. https://doi.org/10.37193/cjm.2019.01.01
| Authors | Andrica, D. and Bagdasar, O. |
|---|---|
| Abstract | In this paper we define the $n$th polygonal polynomial $P_n(z) = (z-1)(z^2-1)\cdots(z^n-1)$ and we investigate recurrence relations and exact integral formulae for the coefficients of $P_n(z)$ and for those of the Mahonian polynomials $Q_n(z)=(z+1)(z^2+z+1)\cdots(z^{n-1}+\cdots+z+1)$. We also explore numerical properties of these coefficients, unraveling new meanings for old sequences and generating novel entries to the Online Encyclopedia of Integer Sequences (OEIS). Some open questions are also formulated. |
| Keywords | Polygonal polynomial; Coefficients; Partitions; Integral formula; Recursive formula; Integer sequences; Asymptotic formula |
| Year | 2019 |
| Journal | Carpathian Journal of Mathematics |
| Journal citation | Vol 35 (Issue 1), pp. 1-12 |
| Publisher | Technical University of Cluj-Napoca. |
| SINUS Association | |
| ISSN | 1584-2851 |
| 1843-4401 | |
| Digital Object Identifier (DOI) | https://doi.org/10.37193/cjm.2019.01.01 |
| Web address (URL) | http://www.scopus.com/inward/record.url?eid=2-s2.0-85063627506&partnerID=MN8TOARS |
| Output status | Published |
| Publication dates | 2019 |
| Publication process dates | |
| Accepted | 03 Nov 2018 |
| Deposited | 15 Feb 2019, 09:16 |
| Contributors | Babeș-Bolyai University and University of Derby |
| File | File Access Level Open |
| File | File Access Level Open |
| File | File Access Level Open |
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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