American Mathematical Monthly · 2011 · 15 citations · 3 references
Natural SciencesComputer ScienceMathematicsAlgebraAlgorithmsCombinatoricsCombinatorial Number TheoryEnumerative CombinatoricsFarey SequencesRational NumbersRecurrence RelationsRecursion TheoryFarey Sequence Recurrence RelationsInteger SequencesLinear Recurrence RelationsRational SeriesSequence EnumerationStern-brocot Tree
The rationals can be enumerated using Stern-Brocot sequences 풮ℬn, Calkin-Wilf sequences 풞풲n, or Farey sequences ℱn. We show that the rationals in 풮ℬn, 풞풲n, and ℱn can be computed using very similar second-order linear recurrence relations. (This, incidentally, obviates the need to compute previous sequences 풮ℬi, 풞풲i, ℱi with i < n.)
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Neil J. Calkin, Herbert S. Wilf · American Mathematical Monthly · 2000 · 196 citations
Exact arithmetic on the Stern–Brocot tree
Milad Niqui · Journal of Discrete Algorithms · 2006 · 28 citations
Locating terms in the Stern–Brocot tree
Bruce Bates, M. W. Bunder, Keith Tognetti · European Journal of Combinatorics · 2009 · 20 citations