@article{9098,
abstract = {We study properties of the volume of projections of the n-dimensional
cross-polytope $\crosp^n = \{ x \in \R^n \mid |x_1| + \dots + |x_n| \leqslant 1\}.$ We prove that the projection of $\crosp^n$ 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 $\crosp^n$ onto a k-dimensional subspace for any n>k⩾2.},
author = {Ivanov, Grigory},
issn = {0012365X},
journal = {Discrete Mathematics},
number = {5},
publisher = {Elsevier},
title = {{On the volume of projections of the cross-polytope}},
doi = {10.1016/j.disc.2021.112312},
volume = {344},
year = {2021},
}