On the Banach-mazur Distance between the Cube and the Crosspolytope
نویسنده
چکیده
In this note we study the Banach-Mazur distance between the n-dimensional cube and the crosspolytope. Previous work shows that the distance has order √ n, and here we will prove some explicit bounds improving on former results. Even in dimension 3 the exact distance is not known, and based on computational results it is conjectured to be 9 5 . Here we will also present computerbased potential optimal results in dimension 4 to 8.
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