Results 41 to 50 of about 8,689,572 (269)
On a new congruence in the Catalan triangle [PDF]
Notes on Number Theory and Discrete MathematicsFor 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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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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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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Structure and Function of a Multi‐Megadalton Virus‐Like Proteolytic Dodecahedron
Angewandte Chemie, EarlyView.Zuzalysin, a virulence metallopeptidase of the periodontal pathogen Porphyromonas gingivalis, is secreted as a latent, flexible ≈95‐kDa monomer. Calcium triggers cysteine‐switch activation and hierarchical assembly into pentamers, bipentamers, tripentamers, and a ≈5.6‐MDa, ≈355‐Å dodecahedron. Structures at 1.8–3.6 Å reveal a virus‐sized catalytic cage
Mariusz Madej +20 more
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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 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.
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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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Angewandte Chemie, EarlyView.Outstanding catalytic results for NH3 decomposition for H2 production were obtained with metallic Ru, Rh, and RuRh nanoparticle‐exsolved CeO2‐based catalysts. Significant lower amounts of available superficial metallic fractions were needed in comparison to conventional Ru‐impregnated materials.
Andrés López‐García +8 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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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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