On Shapiro ' s Cyclic Inequality for N =
نویسنده
چکیده
A cyclic sum S(x) ■ T.x¡/(xj+i + x, + 2) 's formed with the N components of a vector x, where xN+l « JCj, xN+2 =• x2, and where all denominators are positive and all numerators are nonnegative. It is known that there exist vectors x for which S(x) < N/2 if N > 14 and even, and if N > 25. It has been proved that the inequality S(\) > N/2 holds for N ^ 12. 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 N = 13.
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