ON THE BANACH-MAZUR DISTANCE BETWEEN THE CUBE AND THE CROSSPOLYTOPE

被引：5
|
作者：
Xue, Fei [1 ]
机构：
[1] Tech Univ Berlin, Inst Math, Sekr Ma 4-1,Str 17 Juni 136, D-10623 Berlin, Germany
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2018年 / 21卷 / 04期
关键词：
Banach-Mazur distance; cube; crosspolytope; Hadamard matrix;
D O I：
10.7153/mia-2018-21-63
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 root 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 computer based potentially optimal results in dimension 4 to 8.
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页码：931 / 943
页数：13
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