Abstract
It is proved that for anyN ×N orthogonal matrixA = {a ij} we have $$\sum\limits_{i = 1}^N {\mathop {\max }\limits_{1 \leqslant n \leqslant N} |\left| {\sum\limits_{j = 1}^n {a_{ij} } } \right|} \geqslant \frac{1}{{30}}N^{1/2} \log N.$$ A multidimensional analog of this result is also established.
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