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A Combinatorial Interpretation of Ramanujan's Continued Fraction

Published online by Cambridge University Press:  20 November 2018

G. Szekeres
G. Szekeres*
Affiliation:
University of New South Wales
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The purpose of the present note is to give a combinatorial interpretation of the coefficients of expansion of the Ramanujan continued fraction ([1], p. 295)

The result is expressed by formula (12) below.

The enumeration of distinct score vectors of a tournament leads to the following problem: (Erdős and Moser, see Moon [2], p. 68). Given n ≥ 1, k ≥ 0, determine the number of distinct sequences of positive integers

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 3 , August 1968 , pp. 405 - 408
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Hardy, G.H. and Wright, E.M., An introduction to the theory of numbers. 3rd ed. (Oxford, Clarendon Press 1954).Google Scholar
2. Moon, J. W., Topics on tournaments. (Holt, Rinehart and Winston, New York, 1968).Google Scholar