Name
Abstract | ||
|---|---|---|
The present paper deals with the problem of computing (or at least estimating) the (mathrm {LW})-number (lambda (n)), i.e., the supremum of all (gamma ) such that for each convex body K in ({mathbb {R}}^n) there exists an orthonormal basis ({u_1,ldots ,u_n}) such that $$begin{aligned} {text {vol}}_n(K)^{n-1} ge gamma prod _{i=1}^n {text {vol}}_{n-1} , end{aligned}$$where (K|u_i^{perp }) denotes the orthogonal projection of K onto the hyperplane (u_i^{perp }) perpendicular to (u_i). Any such inequality can be regarded as a reverse to the well-known 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)) and deal with the problem of actually computing the (mathrm {LW})-constant of a rational polytope. |
Year | DOI | Venue |
|---|---|---|
2018 | https://doi.org/10.1007/s00454-017-9949-9 | Discrete & Computational Geometry |
Keywords | Field | DocType |
Loomis–Whitney inequality,Convex body,Projection,Volume,Smallest enclosing box,Algorithms,52A20,52A40,68U05 | Combinatorics,Convex body,Infimum and supremum,Polytope,Loomis–Whitney inequality,Hyperplane,Mathematics,Geometry and topology | Journal |
Volume | Issue | ISSN |
60 | 1 | 0179-5376 |
Citations | PageRank | References |
0 | 0.34 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stefano Campi | 1 | 3 | 0.79 |
| Peter Gritzmann | 2 | 412 | 46.93 |
| Paolo Gronchi | 3 | 15 | 4.03 |