Zobrazeno 1 - 9
of 9
pro vyhledávání: '"Manjil P. Saikia"'
Autor:
Pankaj Jyoti Mahanta, Manjil P. Saikia
Publikováno v:
International Journal of Number Theory. 18:1131-1142
Recently, Merca and Yee proved some partition identities involving two new partition statistics. We refine these statistics and generalize the results of Merca and Yee. We also correct a small mistake in a result of Merca and Yee.
Comment: 10 pa
Comment: 10 pa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::00f75e47c638cfc71afecec3e4f462ef
https://doi.org/10.1142/s1793042122500592
https://doi.org/10.1142/s1793042122500592
Publikováno v:
Journal of Number Theory. 217:218-236
Generalizing the concept of a perfect number is a Zumkeller or integer perfect number that was introduced by Zumkeller in 2003. The positive integer $n$ is a Zumkeller number if its divisors can be partitioned into two sets with the same sum, which w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a9861f4f931faab352dbf2f817dfd7c1
https://doi.org/10.1016/j.jnt.2020.05.003
https://doi.org/10.1016/j.jnt.2020.05.003
Autor:
Koustav Banerjee, Sreerupa Bhattacharjee, Manosij Ghosh Dastidar, Pankaj Jyoti Mahanta, Manjil P. Saikia
Publikováno v:
Pankaj Jyoti Mahanta
Let $p_{o}(n)$ (resp. $p_{e}(n)$) denote the number of partitions of $n$ with more odd parts (resp. even parts) than even parts (resp. odd parts). Recently, Kim, Kim, and Lovejoy proved that $p_{o}(n)>p_{e}(n)$ for all $n>2$ and conjectured that $d_{
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fa348ca2800573c46b56cbe7b6783e06
https://orca.cardiff.ac.uk/id/eprint/148447/1/parity_Final.pdf
https://orca.cardiff.ac.uk/id/eprint/148447/1/parity_Final.pdf
Autor:
Pankaj Jyoti Mahanta, Manjil P. Saikia
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards the end of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bf6270f7f7c61e16dd16253adfba64fe
Autor:
Parama Dutta, Manjil P. Saikia
For a positive integer $n$, if $\sigma(n)$ denotes the sum of the positive divisors of $n$, then $n$ is called a deficient perfect number if $\sigma(n)=2n-d$ for some positive divisor $d$ of $n$. In this paper, we prove some results about odd deficie
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::10b13b15e49eeeb9f1bd5f7f9bc7202a
Autor:
Manjil P. Saikia, Alexandre Laugier
Publikováno v:
Demonstratio Mathematica, Vol 49, Iss 3, Pp 266-270 (2016)
We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1d8b434e47babd8c352fb76f438ac606
http://www.degruyter.com/view/j/dema.2016.49.issue-3/dema-2016-0022/dema-2016-0022.xml?format=INT
http://www.degruyter.com/view/j/dema.2016.49.issue-3/dema-2016-0022/dema-2016-0022.xml?format=INT
Publikováno v:
WALCOM: Algorithms and Computation ISBN: 9783030105631
WALCOM
WALCOM
We study tilings of regions in the square lattice with L-shaped trominoes. Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we identify restrictions to the problem where it either rem
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::32b906cbd82c0e7fdc471d30b436f630
http://arxiv.org/abs/1710.04640
http://arxiv.org/abs/1710.04640
In this article, based on ideas and results by J. S\'andor (2001, 2004), we define $k$-multiplicatively $e$-perfect numbers and $k$-multiplicatively $e$-superperfect numbers and prove some results on them. We also characterize the $k$-$T_0T^\ast$-per
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::426d757e86ad079fd4c3149b92a0a2d7
http://arxiv.org/abs/1603.04382
http://arxiv.org/abs/1603.04382
Autor:
Manjil P. Saikia, Alexandre Laugier
In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for $F_p$, where $p$ is a prime of a certain type. We also define period of a Fibonacci sequence modulo an i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d981663b840b262c16ab77c416281b62