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In number theory, the Calkin–Wilf tree is a tree in which the vertices correspond 1-for-1 to the positive rational numbers. The tree is rooted at the number 1, and any rational number expressed in simplest terms as the fraction a/b has as its two children the numbers a/(a + b) and (a + b)/b. Every positive rational number appears exactly once in the tree.

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  • Дерево Калкина — Уилфа
  • Calkin–Wilf tree
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  • Дерево Ка́лкина — Уи́лфа (англ. Calkin—Wilf tree) — ориентированное двоичное дерево, в вершинах которого расположены положительные рациональные дроби согласно следующему правилу: * корень дерева — дробь ; * вершина с дробью имеет двух потомков: (левый) и (правый). Дерево описано Нейлом Калкином и Гербертом С. Уилфом (2000) в связи с задачей явного пересчёта множества рациональных чисел.
  • In number theory, the Calkin–Wilf tree is a tree in which the vertices correspond 1-for-1 to the positive rational numbers. The tree is rooted at the number 1, and any rational number expressed in simplest terms as the fraction a/b has as its two children the numbers a/(a + b) and (a + b)/b. Every positive rational number appears exactly once in the tree.
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  • Дерево Ка́лкина — Уи́лфа (англ. Calkin—Wilf tree) — ориентированное двоичное дерево, в вершинах которого расположены положительные рациональные дроби согласно следующему правилу: * корень дерева — дробь ; * вершина с дробью имеет двух потомков: (левый) и (правый). Дерево описано Нейлом Калкином и Гербертом С. Уилфом (2000) в связи с задачей явного пересчёта множества рациональных чисел.
  • In number theory, the Calkin–Wilf tree is a tree in which the vertices correspond 1-for-1 to the positive rational numbers. The tree is rooted at the number 1, and any rational number expressed in simplest terms as the fraction a/b has as its two children the numbers a/(a + b) and (a + b)/b. Every positive rational number appears exactly once in the tree. The sequence of rational numbers in a breadth-first traversal of the Calkin–Wilf tree is known as the Calkin–Wilf sequence. Its sequence of numerators (or, offset by one, denominators) is Stern's diatomic series, and can be computed by the fusc function. The Calkin–Wilf tree is named after Neil Calkin and Herbert Wilf, who considered it in their 2000 paper. The tree was introduced earlier by Jean Berstel and Aldo de Luca as Raney tree, since they drew some ideas from a paper by George N. Raney. Stern's diatomic series was formulated much earlier by Moritz Abraham Stern, a 19th-century German mathematician who also invented the closely related Stern–Brocot tree.
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  • Calkin–Wilf Tree
  • Stern's Diatomic Series
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  • Calkin-WilfTree
  • SternsDiatomicSeries
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