Combinatorial aspects of continued fractions
نویسندگان
چکیده
منابع مشابه
Combinatorial aspects of continued fractions
We show that the universal continued fraction of the Stieltjes-Jacobi type is equivalent to the characteristic series of labelled paths in the plane . The equivalence holds in the set of series in non-commutative indeterminates . Using it, we derive direct combinatorial proofs of continued fraction expansions for series involving known combinatorial quantities : the Catalan numbers, the Bell an...
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In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...
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We investigate some of the connections between continued fractions and continued logarithms. We study the binary continued logarithms as introduced by Bill Gosper and explore two generalizations of the continued logarithm to base b. We show convergence for them using equivalent forms of their corresponding continued fractions. Through numerical experimentation we discover that, for one such for...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1980
ISSN: 0012-365X
DOI: 10.1016/0012-365x(80)90050-3