Results 61 to 70 of about 1,655,826 (313)
Some properties of the Catalan numbers
Applicable Analysis and Discrete MathematicsThis 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
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Generalized $q,t$-Catalan numbers [PDF]
Algebraic Combinatorics, 2019 Author(s): Gorsky, Eugene; Hawkes, Graham; Schilling, Anne; Rainbolt, Julianne | Abstract: Recent work of the first author, Negut and Rasmussen, and of Oblomkov and Rozansky in the context of Khovanov--Rozansky knot homology produces a family of ...
E. Gorsky +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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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
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Generalized Catalan Numbers and Some Divisibility Properties [PDF]
, 2015 I investigate the divisibility properties of generalized Catalan numbers by ex- tending known results for ordinary Catalan numbers to their general case. First, I define the general Catalan numbers and provide a new derivation of a known formula. Second,
Bobrowski, Jacob
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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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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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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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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 +3 more
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Advanced Materials, EarlyView.AI‐Assisted Workflow for (Scanning) Transmission Electron Microscopy: From Data Analysis Automation to Materials Knowledge Unveiling. Abstract (Scanning) transmission electron microscopy ((S)TEM) has significantly advanced materials science but faces challenges in correlating precise atomic structure information with the functional properties of ...
Marc Botifoll +19 more
wiley +1 more source