Results 41 to 50 of about 19,167 (257)

Growing and Destroying Catalan-Stanley Trees [PDF]

Discrete Mathematics & Theoretical Computer Science, 2018
Stanley lists the class of Dyck paths where all returns to the axis are of odd length as one of the many objects enumerated by (shifted) Catalan numbers.
Benjamin Hackl, Helmut Prodinger
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Simplifying coefficients in differential equations for generating function of Catalan numbers

Journal of Taibah University for Science, 2019
In the paper, by the Faà di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients in two families of nonlinear ordinary differential equations for the generating ...
Feng Qi, Yong-Hong Yao
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On a new congruence in the Catalan triangle [PDF]

Notes on Number Theory and Discrete Mathematics
For 0≤k≤n, the number C(n,k) represents the number of all lattice paths in the plane from the point (0,0) to the point (n,k), using steps (1,0) and (0,1), that never rise above the main diagonal y = x.
Jovan Mikić
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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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On the $H$-triangle of generalised nonnesting partitions [PDF]

Discrete Mathematics & Theoretical Computer Science, 2014
With a crystallographic root system $\Phi$ , there are associated two Catalan objects, the set of nonnesting partitions $NN(\Phi)$, and the cluster complex $\Delta (\Phi)$. These possess a number of enumerative coincidences, many of which are captured in
Marko Thiel
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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.
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The Problem of Separatism in Modern Spain: the Catalan Question

Проблемы постсоветского пространства, 2022
Catalan nationalism, rooted in the 19th century, transformed into separatism in the 1980s, threatening the existence of the Spanish state. The unstable political situation in the country caused by the crisis of the party system and serious economic ...
S. M. Gavrilova
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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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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 ...
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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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