On Shapiro's cyclic inequality for

Author:
B. A. Troesch

Journal:
Math. Comp. **45** (1985), 199-207

MSC:
Primary 26D15; Secondary 05A20

DOI:
https://doi.org/10.1090/S0025-5718-1985-0790653-0

MathSciNet review:
790653

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Abstract: A cyclic sum is formed with the *N* components of a vector **x**, where , , and where all denominators are positive and all numerators are nonnegative. It is known that there exist vectors **x** for which if and even, and if . It has been proved that the inequality holds for . Although it has been conjectured repeatedly that the inequality also holds for odd *N* between 13 and 23. this has apparently not yet been proved. Here we will confirm that the inequality indeed holds for .

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1985-0790653-0

Keywords:
Cyclic inequality,
cyclic sum,
minimization

Article copyright:
© Copyright 1985
American Mathematical Society