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Catalan number

The Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after Eugène Catalan, though they were previously discovered in the 1730s by Minggatu.

History & Applications

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Overview

Properties

Applications in combinatorics

Proof of the formula

Hankel matrix

History

Generalizations

Advanced semantic analysis

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Map overview Semantic statistics

Catalan number

Nodes68
Edges67
Triples143
Avg. degree1.97
Density0.029412
Components1

How this topic connects Entity context

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Catalan number

Top relations

related to References · 46
Catalan number → Advanced Mathematics, Applications, Bibcode, Cambridge Studies, Cambridge University Press, Catalan, Catalan Numbers, Ch, Chinese, Company, Conway, Copernicus, Enumerative, Fourth Kind, Freeman, Gardner, Gheorghiciuc, Gidon, Guy, Hankel Determinant Evaluation
related to External links · 19
Catalan number → Catalan, Davis, Enumerative Combinatorics, Equivalence, Eric, Learning, MathWorld, Partition, PDF, Richard, Stanley, Still, The Wolfram Demonstrations Project, Three Catalan Number Interpretations, Tom, Volume, Weisstein, Wikiversity, Wiktionary-logo-en-v2
related to Sixth proof · 19
Catalan number → Catalan, Dvoretzky, Dyck, Each, For, Motzkin, Repeatedly, The, This, To, We, Xs, XXYXY, XY, XYXXY, XYXYX, Ys, YXXYX, YXYXX
has application · 15
Catalan number → C3, C4, Catalan, Cn, Dyck, Enumerative Combinatorics, Following, For, Richard, Stanley, The, There, Volume, X's, Y's
related to history · 10
Catalan number → Catalan, Dyck, Désiré André, Eugène Charles Catalan, Hanoi, John Riordan, Leonhard Euler, The, The Catalan, Towers
related to Generalizations · 9
Catalan number → Bertrand's, Catalan, Hipparchus, Ira Gessel, Schröder, Specifically, The, The Catalan, These
related to Fifth proof · 8
Catalan number → Bn, Catalan, Cn, Dyck, Let, Since, This, We
related to Hankel matrix · 6
Catalan number → Catalan, Ci, For, Hankel, Moreover, The
see also · 6
Catalan number → AssociahedronBertrand's, Catalan, Etherington, Hipparchus, Mathematics, Mersenne
related to Fourth proof · 5
Catalan number → Catalan, Cn, Given, There, This

Important terminology Word statistics

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Important terminology

catalan number displaystyle numbers 2n cn path frac first sequence binom given dyck one sum words monotonic paths ways diagonal

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Catalan numberhas applicationThere0.60section
Catalan numberhas applicationCatalan0.60section
Catalan numberhas applicationThe0.60section
Catalan numberhas applicationEnumerative Combinatorics0.60section
Catalan numberhas applicationVolume0.60section
Catalan numberhas applicationRichard0.60section
Catalan numberhas applicationStanley0.60section
Catalan numberhas applicationFollowing0.60section
Catalan numberhas applicationC30.60section
Catalan numberhas applicationC40.60section
Catalan numberhas applicationCn0.60section
Catalan numberhas applicationDyck0.60section

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    Min side: 3
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