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Continuants with bounded digits

Published online by Cambridge University Press:  26 February 2010

T. W. Cusick
T. W. Cusick
Affiliation:
State University of New York at Buffalo.
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Extract

We let K(a1a2, ak) denote the continuant formed from the positive integers a1 …, ak; that is,

Of course, K(a1, …, an) is the denominator of the continued fraction

We use the convention that K (empty set) = 1.

Type
Research Article
Information
Mathematika , Volume 24 , Issue 2 , December 1977 , pp. 166 - 172
Copyright
Copyright © University College London 1977

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References

1.Borosh, I.. “Rational continued fractions with small partial quotients”, Notices Amer. Math. Soc., 23 (1976), abstract 731–10–29, p. A-52.Google Scholar
2.Bumby, R. T.. “Dimensions of sets of continued fractions”, unpublished manuscript, 1975.Google Scholar
3.Good, I. J.. “The fractional dimension theory of continued fractions”, Proc. Cambridge Philos. Soc., 37 (1941), 199–228.CrossRefGoogle Scholar
4.Motzkin, T. S. and Straus, E. G.. “Some combinatorial extremum problems”, Proc. Amer. Math. Soc., 7 (1956), 1014–1021.CrossRefGoogle Scholar