On Shapiro's cyclic inequality for
Author:
B. A. Troesch
Journal:
Math. Comp. 45 (1985), 199207
MSC:
Primary 26D15; Secondary 05A20
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:
http://dx.doi.org/10.1090/S00255718198507906530
PII:
S 00255718(1985)07906530
Keywords:
Cyclic inequality,
cyclic sum,
minimization
Article copyright:
© Copyright 1985 American Mathematical Society
