Results 41 to 50 of about 1,693 (108)

Normal ordering associated with λ-Stirling numbers in λ-shift algebra

Demonstratio Mathematica, 2023
It is known that the Stirling numbers of the second kind are related to normal ordering in the Weyl algebra, while the unsigned Stirling numbers of the first kind are related to normal ordering in the shift algebra.
Kim Taekyun, Kim Dae San, Kim Hye Kyung
doaj   +1 more source

The second production matrix of a Riordan array [PDF]

arXiv, 2020
A Riordan array is defined by its production matrix. In this paper, we explore the notion of the second production matrix of a Riordan array, characterizing the matrix that is generated by it. We indicate how this procedure can be generalized to the so-called $n$-th production matrix of a Riordan array.
arxiv  

Compositions of positive integers with 2s and 3s

Demonstratio Mathematica, 2023
In this article, we consider compositions of positive integers with 2s and 3s. We see that these compositions lead us to results that involve Padovan numbers, and we give some tiling models of these compositions.
Dişkaya Orhan, Menken Hamza
doaj   +1 more source

Some identities for the Narayana polynomial and its derivatives [PDF]

arXiv, 2022
In this note, by employing a nice property of semicircular distributions, we derive some identities for the Narayana polynomial and its derivatives.
arxiv  

A note on OEIS sequence A111384 [PDF]

arXiv, 2023
$A111384(n)$ is an upper bound for the number of primes that can be written as a sum of three distinct primes selected from a set of $n$ primes. Is this bound sharp?
arxiv  

A q-rious positivity

, 2010
The $q$-binomial coefficients $\qbinom{n}{m}=\prod_{i=1}^m(1-q^{n-m+i})/(1-q^i)$, for integers $0\le m\le n$, are known to be polynomials with non-negative integer coefficients.
Warnaar, S. Ole, Zudilin, Wadim
core   +1 more source

Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants [PDF]

, 2012
MSC 2010: 11B83, 05A19, 33C45This paper is dealing with the Hankel determinants of the special number sequences given in an integral form. We show that these sequences satisfy a generalized convolution property and the Hankel determinants have the ...
Barry, Paul, Rajkovic, Predrag M., Savic, Natasa   +2 more
core  

Galois Identities of the three term recurrence [PDF]

, 2013
We study the existence of the identity L_n^2 -5F_n^2 = 4(-1 ...
Cheng Lien, Lang, Mong Lung Lang
core  

Enumerating the rationals from left to right

, 2010
Farey sequences, Stern-Brocot sequences, the Calkin-Wilf sequences are shown to be generated via almost identical second order recurrence relations.
Glasby, S. P.
core   +1 more source

Zeros distribution and interlacing property for certain polynomial sequences

Open Mathematics
In this article, we first prove that the Hankel determinant of order three of the polynomial sequence {Pn(x)=∑k≥0P(n,k)xk}n≥0{\left\{{P}_{n}\left(x)={\sum }_{k\ge 0}P\left(n,k){x}^{k}\right\}}_{n\ge 0} is weakly (Hurwitz) stable, where P(n,k)P\left(n,k ...
Guo Wan-Ming
doaj   +1 more source