Neighboring Fractions in Farey Subsequences
نویسنده
چکیده
We present explicit formulas for computation of the neighbors of several elements in Farey subsequences.
منابع مشابه
On Boolean Lattices and Farey Sequences
We establish monotone bijections between subsequences of the Farey sequences and the halfsequences of Farey subsequences associated with elements of the Boolean lattices.
متن کاملA Note on Boolean Lattices and Farey Sequences. Ii
We establish monotone bijections between subsequences of the Farey sequences and the halfsequences of Farey subsequences associated with elements of the Boolean lattices.
متن کامل2 00 8 a Note on Boolean Lattices and Farey Sequences . Ii
We establish monotone bijections between subsequences of the Farey sequences and the halfsequences of Farey subsequences associated with elements of the Boolean lattices.
متن کاملA Note on Boolean Lattices and Farey Sequences
We establish monotone bijections between the Farey sequences of order m and the halfsequences of Farey subsequences associated with the rank m elements of the Boolean lattice of subsets of a 2m-set. We also present a few related combinatorial identities. Subject class: 05A19, 11B65.
متن کاملOn the Index of Farey Sequences
For any two consecutive Farey fractions γi = ai/qi < γi+1 = ai+1/qi+1, one has ai+1qi − aiqi+1 = 1 and qi + qi+1 > Q. Conversely, if q and q ′ are two coprime integers in {1, . . . , Q} with q + q > Q, then there are unique a ∈ {1, . . . , q} and a ∈ {1, . . . , q} for which aq − aq = 1, and a/q < a/q are consecutive Farey fractions of order Q. Therefore, the pairs of coprime integers (q, q) wi...
متن کامل