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On the volume of projections of the cross-polytope
Discrete Mathematics ( IF 0.7 ) Pub Date : 2021-02-01 , DOI: 10.1016/j.disc.2021.112312
Grigory Ivanov

We study properties of the volume of projections of the n-dimensional cross-polytope n={xRn|x1|++|xn|1}. We prove that the projection of n onto a k-dimensional coordinate subspace has the maximum possible volume for k=2 and for k=3. We obtain the exact lower bound on the volume of such a projection onto a two-dimensional plane. Also, we show that there exist local maxima which are not global ones for the volume of a projection of n onto a k-dimensional subspace for any n>k2.



中文翻译:

关于交叉多面体的投影量

我们研究了投影的体积特性 ñ维交叉多态性 ñ={X[Rñ|X1个|++|Xñ|1个}。我们证明ñ 到一个 ķ维坐标子空间具有最大可能的体积 ķ=2 和为 ķ=3我们获得了这种投影到二维平面上的体积的确切下界。此外,我们表明存在局部最大值,对于投影的体积,该最大值不是全局最大值ñ 到一个 ķ维子空间 ñ>ķ2

更新日期:2021-02-01
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