Statements (54)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
mathematical system
|
| gptkbp:appliesTo |
counting problems
|
| gptkbp:description |
gptkb:Catalan_numbers
|
| gptkbp:hasAccessTo |
C(n) = (2n)! / ((n+1)!n!)
|
| gptkbp:hasRelatedPatent |
algorithm analysis
computer science dynamic programming graph theory |
| gptkbp:hasSpecialty |
asymptotic behavior
non-negative integers closed under certain operations exponential generating function |
| https://www.w3.org/2000/01/rdf-schema#label |
Catalan System
|
| gptkbp:includes |
binary trees
parentheses matching Dyck words polygon_triangulation |
| gptkbp:isA |
mathematical concept
sequence sequence of numbers combinatorial object counting sequence |
| gptkbp:isCitedBy |
recurrence relation
|
| gptkbp:isCounteredBy |
gptkb:Catalan_numbers
|
| gptkbp:isImportantFor |
mathematical logic
theory of computation discrete mathematics |
| gptkbp:isLocatedIn |
C(n) = Σ C(i)C(n-i-1) for i=0 to n-1
terms of binomial coefficients terms of factorials terms of generating functions terms of recurrence relations |
| gptkbp:isNamedAfter |
gptkb:Eugène_Charles_Catalan
|
| gptkbp:isRelatedTo |
binomial coefficients
tree structures combinatorial structures Fibonacci numbers lattice paths |
| gptkbp:isStudiedIn |
computer science
mathematics combinatorial theory |
| gptkbp:isUsedFor |
counting paths in a grid
counting triangulations of polygons counting valid parentheses combinations counting ways to connect points |
| gptkbp:isUsedIn |
algorithm design
data structures mathematical modeling optimization problems mathematical proofs combinatorial proofs combinatorial_enumeration |
| gptkbp:namedAfter |
gptkb:Eugène_Charles_Catalan
|
| gptkbp:relatedTo |
combinatorial mathematics
|