@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},
}