Results 31 to 40 of about 7,617 (257)
Alternating Convolutions of Catalan Numbers [PDF]
Bulletin of the Brazilian Mathematical Society, New Series, 2021 A new class of alternating convolutions concerning binomial coefficients and Catalan numbers are evaluated in closed forms.
openaire +3 more sources
On powers of the Catalan number sequence [PDF]
Discrete Mathematics, 2019 The Catalan number sequence is one of the most famous number sequences in combinatorics and is well studied in the literature. In this paper we further investigate its fundamental properties related to the moment problem and prove for the first time that it is an infinitely divisible Stieltjes moment sequence in the sense of S.-G. Tyan.
openaire +3 more sources
Catalan numbers, q-Catalan numbers and hypergeometric series
Journal of Combinatorial Theory, Series A, 1987 The author derives a new \(q\)-analog of the Catalan numbers: \[ {\mathcal C}_ n(\lambda,q)=q^{2n}\prod \frac{1+\lambda q^{2i-3}}{1-q^{2i}},\quad 1\leq i\leq n. \] The usual Catalan numbers are given by \({\mathcal C}_ n={\mathcal C}_ n(-1,1)\). In addition to this representation as a rational function in \(q\), Andrews' \(q\)-Catalan numbers have a ...
openaire +1 more source
Modular Fuss-Catalan numbers [PDF]
Discrete Mathematics, 2022 The modular Catalan numbers $C_{k,n}$, introduced by Hein and Huang in 2016 count equivalence classes of parenthesizations of $x_0 * x_1 * \dots *x_n$ where $*$ is a binary $k$-associative operation and $k$ is a positive integer. The classical notion of associativity is just 1-associativity, in which case $C_{1,n} = 1$ and the size of the unique class ...
openaire +4 more sources
One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers
Annales Mathematicae Silesianae, 2023 In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover,
Bród Dorota +2 more
doaj +1 more source
Volterra Chain and Catalan Numbers [PDF]
JETP Letters, 2018 4 pages, 2 ...
Adler, V. E., Shabat, A. B.
openaire +2 more sources
On generalised catalan numbers
Discrete Mathematics, 1978 AbstractThe Catalan number Cn is defined to be 2nn(n+1). One of its occurrences is as the number of ways of bracketing a product of n+1 terms taken from a set with binary operation. In this note the corresponding result for a set with a k-ary operation is considered.
openaire +2 more sources
Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers
Journal of Mathematics, 2023 In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties.
Kübra Gül
doaj +1 more source
Advanced Materials, EarlyView.The Y supersaturation in the [Ba‐Cu(I/II)‐O] transient liquid composition is the driving force toward YBCO nucleation and growth in TLAG. Tuning the initial (Ba:Cu) molar ratio in the ink composition determines the YBCO epitaxial nucleation through supersaturation control.
Lavinia Saltarelli +12 more
wiley +1 more source
$q,t$-Fuß-Catalan numbers for complex reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 In type $A$, the $q,t$-Fuß-Catalan numbers $\mathrm{Cat}_n^{(m)}(q,t)$ can be defined as a bigraded Hilbert series of a module associated to the symmetric group $\mathcal{S}_n$.
Christian Stump
doaj +1 more source