Results 31 to 40 of about 107,847 (314)
A Note on Super Catalan Numbers [PDF]
Interdisciplinary Information Sciences, 2012 4 pages. Revised and Accepted. To appear in Interdisciplinary Information Sciences (IIS)
Evangelos Georgiadis +2 more
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The NADPH oxidase NOX4 regulates redox and metabolic homeostasis preventing HCC progression
Hepatology, EarlyView., 2022 Loss of NOX4 in HCC tumor cells induces metabolic reprogramming in a Nrf2/MYC‐dependent manner to promote HCC progression. Abstract Background and Aims The NADPH oxidase NOX4 plays a tumor‐suppressor function in HCC. Silencing NOX4 confers higher proliferative and migratory capacity to HCC cells and increases their in vivo tumorigenic potential in ...
Irene Peñuelas‐Haro +14 more
wiley +1 more source
Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$ [PDF]
Notes on Number Theory and Discrete MathematicsWe find various series that involve the central binomial coefficients $binom{2n}{n}$, harmonic numbers and Fibonacci numbers. Contrary to the traditional hypergeometric function _pF_q approach, our method utilizes a straightforward transformation to ...
Segun Olofin Akerele +1 more
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Volterra Chain and Catalan Numbers [PDF]
JETP Letters, 2018 4 pages, 2 ...
Alexey Borisovich Shabat +1 more
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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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Integral Representations of the Catalan Numbers and Their Applications
Mathematics, 2017 In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations ...
Feng Qi, Bai-Ni Guo
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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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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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Catalan pairs: A relational-theoretic approach to Catalan numbers
Advances in Applied Mathematics, 2010 AbstractWe define the notion of a Catalan pair (which is a pair of binary relations (S,R) satisfying certain axioms) with the aim of giving a common language to several combinatorial interpretations of Catalan numbers. We show, in particular, that the second component R uniquely determines the pair, and we give a characterization of R in terms of ...
DISANTO, FILIPPO +3 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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