TY  JOUR
AU1  Campi, Stefano
AU2  Gritzmann, Peter
AU3  Gronchi, Paolo
AB  The present paper deals with the problem of computing (or at least estimating) the
$$\mathrm {LW}$$
LW
number
$$\lambda (n)$$
λ
(
n
)
, i.e., the supremum of all
$$\gamma $$
γ
such that for each convex body K in
$${\mathbb {R}}^n$$
R
n
there exists an orthonormal basis
$$\{u_1,\ldots ,u_n\}$$
{
u
1
,
…
,
u
n
}
such that
$$\begin{aligned} {\text {vol}}_n(K)^{n1} \ge \gamma \prod _{i=1}^n {\text {vol}}_{n1} (Ku_i^{\perp }) , \end{aligned}$$
vol
n
(
K
)
n

1
≥
γ
∏
i
=
1
n
vol
n

1
(
K

u
i
⊥
)
,
where
$$Ku_i^{\perp }$$
K

u
i
⊥
denotes the orthogonal projection of K onto the hyperplane
$$u_i^{\perp }$$
u
i
⊥
perpendicular to
$$u_i$$
u
i
. Any such inequality can be regarded as a reverse to the wellknown classical Loomis–Whitney inequality. We present various results on such reverse Loomis–Whitney inequalities. In particular, we prove some structural results, give bounds on
$$\lambda (n)$$
λ
(
n
)
and deal with the problem of actually computing the
$$\mathrm {LW}$$
LW
constant of a rational polytope.
TI  On the Reverse Loomis–Whitney Inequality
JF  Discrete & Computational Geometry
DO  10.1007/s0045401799499
DA  20171027
UR  https://www.deepdyve.com/lp/springerjournals/onthereverseloomiswhitneyinequalityShJd1CDRH3
SP  115
EP  144
VL  60
IS  1
DP  DeepDyve