Polynomial Bounds in Koldobsky's Discrete Slicing Problem

Freyer, Ansgar; Henk, Martin

doi:10.48550/arXiv.2303.15976

Record link:

http://hdl.handle.net/20.500.12708/189969
https://doi.org/10.34726/5243

Title:

Polynomial Bounds in Koldobsky's Discrete Slicing Problem

Citation:

Freyer, A., & Henk, M. (2023). Polynomial Bounds in Koldobsky’s Discrete Slicing Problem. arXiv. https://doi.org/10.34726/5243

reposiTUm DOI:

10.34726/5243

CatalogPlus:

AC17203281

Publisher DOI:

10.48550/arXiv.2303.15976

Publication Type:

Preprint

Language:

English

Authors:

Freyer, Ansgar
Henk, Martin

Organisational Unit:

E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie

ArXiv ID:

2303.15976

Date (published):

28-Mar-2023

Number of Pages:

Preprint Server:

arXiv

Keywords:

Lattice Width; Slicing Problem; Flatness Theorem

Abstract:

In this article we show that dⁿ is bounded from above by cn²ω(n), where c is an absolute constant and ω(n) is the flatness constant. Due to the best known upper bound on ω(n) this gives a cn¹⁰/³log(n)ᵃ bound on dⁿ where a is another absolute constant. This bound improves on former bounds which were exponential in the dimension.

Project title:

Bewertungen auf konvexen Funktionen: P 34446-N (FWF - Österr. Wissenschaftsfonds)

Research Areas:

Mathematical and Algorithmic Foundations: 100%

Science Branch:

1010 - Mathematik: 100%

License:

CC BY-SA 4.0