Results 31 to 40 of about 112,655 (271)
Volterra Chain and Catalan Numbers [PDF]
JETP Letters, 2018 4 pages, 2 ...
Adler, V. E., Shabat, A. B.
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Generalized Catalan Numbers from Hypergraphs [PDF]
The Electronic Journal of Combinatorics, 2021 The Catalan numbers $C_{n} \in \{1,1,2,5,14,42,\dots \}$ form one of the most venerable sequences in combinatorics. They have many combinatorial interpretations, from counting bracketings of products in non-associative algebra to counting rooted plane trees and noncrossing set partitions.
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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 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 +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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, 2017 Fix an integer partition lambda that has no more than n parts. Let beta be a weakly increasing n-tuple with entries from {1,..,n}. The flagged Schur function indexed by lambda and beta is a polynomial generating function in x_1, .., x_n for certain ...
Proctor, Robert A., Willis, Matthew J.
core +1 more source
Generalized compositions with a fixed number of parts [PDF]
, 2010 We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of the Catalan ...
Janjic, Milan
core
Intersection Numbers on Fibrations and Catalan Numbers
Experimental Mathematics, 2023 On an elliptic surface or threefold, Catalan numbers appear when one tries to compute the autoequivalence group action on the Bridgeland stability manifold. We explain why this happens by identifying a class of equations in the Chow ring of a fibration, where the solutions always involve Catalan numbers.
Rimma Hämäläinen +2 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
Cores with distinct parts and bigraded Fibonacci numbers
, 2017 The notion of $(a,b)$-cores is closely related to rational $(a,b)$ Dyck paths due to Anderson's bijection, and thus the number of $(a,a+1)$-cores is given by the Catalan number $C_a$.
Paramonov, Kirill
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