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. |
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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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https://repository.derby.ac.uk/item/93457/on-some-results-concerning-the-polygonal-polynomials
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