Results 41 to 50 of about 1,690,008 (302)

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.
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Chromatic statistics for Catalan and Fuß-Catalan numbers

Electronic Journal of Combinatorics, 2011
We refine Catalan numbers and Fuß-Catalan numbers by introducing colour statistics for triangulations of polygons and $d$-dimensional generalisations there-of which we call Fuß-Catalan complexes. Our refinements consist in showing that the number of triangulations, respectively Fuß-Catalan complexes, with a given colour distribution of its vertices is ...
Bacher, Roland, Krattenthaler, Christian
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Volterra Chain and Catalan Numbers [PDF]

JETP Letters, 2018
4 pages, 2 ...
Adler, V. E., Shabat, A. B.
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Catalan pairs and Fishburn triples

, 2015
Disanto, Ferrari, Pinzani and Rinaldi have introduced the concept of 'Catalan pair', which is a pair of partial orders (S,R) satisfying certain axioms.
Jelínek, Vít
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Some properties of the Catalan numbers

Applicable Analysis and Discrete Mathematics
This paper is dedicated to my father for his forever health In the paper, the author presents two expansions, complete monotonicity, minimality, some determinantal inequalities, and product inequalities of the Catalan numbers and other sequences ...
Feng Qi
semanticscholar   +1 more source

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, Szynal-Liana Anetta, Włoch Iwona   +2 more
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Enumerating five families of pattern-avoiding inversion sequences; and introducing the powered Catalan numbers [PDF]

Theoretical Computer Science, 2018
The first problem addressed by this article is the enumeration of some families of pattern-avoiding inversion sequences. We solve some enumerative conjectures left open by the foundational work on the topics by Corteel et al., some of these being also ...
N. Beaton, M. Bouvel, V. Guerrini, S. Rinaldi   +3 more
semanticscholar   +1 more source

Catalan pairs: A relational-theoretic approach to Catalan numbers

Advances in Applied Mathematics, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
DISANTO, FILIPPO, Ferrari L, Pinzani R, Rinaldi S.   +3 more
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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 ...
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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
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