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Some Inequalities involving (r!)1/r

Published online by Cambridge University Press:  20 January 2009

Henryk Minc  and
Leroy Sathre
Henryk Minc
Affiliation:
University of California, Santa Barbara
Leroy Sathre
Affiliation:
University of Florida, Gainesville
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In a recent investigation of a conjecture on an upper bound for permanents of (0, 1)-matrices (2) we obtained some inequalities involving the function (r!)1/r which are of interest in themselves. Probably the most interesting of them, and certainly the hardest to prove, is the inequality

where ø(r = (r!)1/r. In the present paper we prove (1) and other inequalities involving the function ø(r.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 1 , June 1964 , pp. 41 - 46
Copyright
Copyright © Edinburgh Mathematical Society 1964

References

REFERENCE

(1) Erdélyi, A. et al. , Higher Transcendental Functions, 1 (New York, 1953).Google Scholar
(2) Minc, Henryk, Upper bounds for permanents of (0, l)-matrices, Bull. Amer. Math. Soc., 69 (1963), 789–791.CrossRefGoogle Scholar