Results 1 to 10 of about 111,861 (267)
AN ALTERNATIVE DECOMPOSITION OF CATALAN NUMBER [PDF]
Facta Universitatis, Series: Mathematics and Informatics, 2018 A particular integer sequence derived by the convex polygon triangulation is introduced and investigated. After some underlying results are presented, the forbidden (or improper) integer values relative to the triangulation are concerned. It is understood that the forbidden sequences do not correspond to any triangulation.
Predrag Krtolica +2 more
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Eulerian-Catalan Numbers [PDF]
The Electronic Journal of Combinatorics, 2011 We show that the Eulerian-Catalan numbers enumerate Dyck permutations. We provide two proofs for this fact, the first using the geometry of alcoved polytopes and the second a direct combinatorial proof via an Eulerian-Catalan analogue of the Chung-Feller theorem.
Bidkhori, Hoda, Sullivant, Seth
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Noncommutative Catalan Numbers [PDF]
Annals of Combinatorics, 2019 The goal of this paper is to introduce and study noncommutative Catalan numbers $C_n$ which belong to the free Laurent polynomial algebra in $n$ generators. Our noncommutative numbers admit interesting (commutative and noncommutative) specializations, one of them related to Garsia-Haiman $(q,t)$-versions, another -- to solving noncommutative quadratic ...
Berenstein, A., Retakh, V.
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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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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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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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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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