Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
combinatorics
|
| gptkbp:definedIn |
lattice path from (0,0) to (2n,0) with steps (1,1) and (1,-1) that never goes below x-axis
|
| gptkbp:enumeratedBy |
gptkb:Catalan_numbers
|
| gptkbp:generalizes |
gptkb:Motzkin_paths
gptkb:Schröder_paths |
| gptkbp:hasApplication |
gptkb:algebra
gptkb:geometry gptkb:probability_theory computer science formal languages |
| gptkbp:hasProperty |
never goes below x-axis
number of up steps equals number of down steps |
| https://www.w3.org/2000/01/rdf-schema#label |
Dyck paths
|
| gptkbp:namedAfter |
gptkb:Walther_von_Dyck
|
| gptkbp:relatedTo |
gptkb:Catalan_numbers
lattice paths binary trees noncrossing partitions parentheses matching |
| gptkbp:studiedBy |
19th century
|
| gptkbp:usedIn |
enumerative combinatorics
|
| gptkbp:visualizes |
mountain range
balanced parentheses binary tree traversal |
| gptkbp:bfsParent |
gptkb:Catalan_numbers
|
| gptkbp:bfsLayer |
7
|