Results 81 to 90 of about 1,269,170 (176)

A determinant property of Catalan numbers

Discrete Mathematics, 2000
Let \(M_k^t\) denote the \(k \times k\) (persymmetric) matrix having the consecutive Catalan numbers starting at \(c_t\) as row one, those starting at \(c_{t+1}\) as row two, etc. Now define \(G\) to be the infinite digraph with vertex set \({\mathbb{Z}} \times {\mathbb{Z}}\) and with directed arcs from \((i,j)\) to \((i+1,j)\), and to \({(i,j+1 ...
Michael E. Mays, Jerzy Wojciechowski
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A Filtration of (q,t)-Catalan numbers

Advances in Applied Mathematics, 2008
We define new generalizations of (q,t)-Catalan numbers applying nabla operator on k-Schur functions indexed by column partitions. In some special cases, we give a combinatorial interpretation of these numbers using configurations of Dyck paths. In some other special cases, we also interpret these new polynomial as Hilbert series of explicit sub-modules
Nantel Bergeron, François Descouens, Mike Zabrocki   +2 more
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Catalan numbers and Pascal's Triangle

, 2017
Die Diplomarbeit behandelt sowohl die Catalan-Zahlen, als auch einige grundsätzliche Ideen des Pascalschen Dreiecks. Nach einem kurzen, historischen Überblick über die Erforschung der Catalan-Zahlen folgen einige Definitionen, die im Laufe der Zeit ...
Unterluggauer, Philipp
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Tableau Cycling and Catalan Numbers

, 2007
We develop two combinatorial proofs of the fact that certain Young tableaux are counted by the Catalan numbers. The setting is a larger class of tableaux where labels increase along rows without attention to whether labels increase down columns. We define a new operation called tableau cycling. It is used to duplicate the reflection argument attributed
Buontempo, Jenny, Hopkins, Brian
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Remarks on Catalan and super-Catalan numbers [PDF]

Banach Center Publications, 2011
Anna Dorota Krystek, Łukasz Jan Wojakowski   +1 more
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Catalan, Motzkin, and Riordan numbers

Discrete Mathematics, 1999
The article presents a unified overview of the Catalan and Motzkin numbers together with a third sequence called Riordan (ring) numbers [see \textit{J. Riordan}, J. Comb. Theory, Ser. A 19, 214-222 (1975; Zbl 0308.05115)], having wide range of applications.
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The catalan premium: language and employment in Catalonia. [PDF]

This paper measures the contribution of knowing Catalan to finding a job in Catalonia. In the early eighties a drastic language policy change (normalització) promoted the learning and use of Catalan and managed to reverse the falling trend of its ...
Rendón, Silvio
core  

Pell Leonardo numbers and their matrix representations

Journal of New Results in Science
In this study, we investigate Pell numbers and Leonardo numbers and describe a new third-order number sequence entitled Pell Leonardo numbers. We then construct some identities, including the Binet formula, generating function, exponential generating ...
Çağla Çelemoğlu
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On a New Generalization of Pell Hybrid Numbers

Annales Mathematicae Silesianae
In this paper, we define and study a new one-parameter generalization of the Pell hybrid numbers. Based on the definition of r-Pell numbers, we define the r-Pell hybrid numbers.
Bród Dorota, Szynal-Liana Anetta, Włoch Iwona   +2 more
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Divisibility of generalized Catalan numbers

Journal of Combinatorial Theory, Series A, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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