Last Updated
：2025/11/25
Dyck word
Noun
Japanese Meaning
n個のXとn個のYからなる文字列で、任意の初期部分においてXの個数がYの個数以上である、すなわちXの数が常にYの数と同等かそれ以上になる条件を満たす文字列。 / この性質は、正しい括弧列の条件と同値であり、括弧の対応関係やバランスの取れた表現を表現するために利用される。
（ plural ）
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(mathematics, combinatorics) A string consisting of n X's and n Y's such that no initial segment of the string has more Y's than X's.
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Dyck word
To count the number of monotonic lattice paths that never cross the diagonal, we encode each path as a Dyck word.
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To count the number of monotonic lattice paths that never cross the diagonal, we encode each path as a Dyck word.
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