Reducing the upper bound for the Borsuk number in $\mathbb{R}^4$ to 8
Fuente:
arXiv
Saved in:
| Main Authors: | Tolmachev, Alexander, Voronov, Vsevolod |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Similar Items
On lower bounds of the density of planar periodic sets without unit distances
by: Tolmachev, Alexander
Published: (2024)
by: Tolmachev, Alexander
Published: (2024)
Lower Bound on Translative Covering Density of Tetrahedra
by: Li, Yiming, et al.
Published: (2022)
by: Li, Yiming, et al.
Published: (2022)
Decomposition method and upper bound density related to congruent saturated hyperball packings in hyperbolic $n-$space
by: Yahya, Arnasli, et al.
Published: (2025)
by: Yahya, Arnasli, et al.
Published: (2025)
No new lower bound for the density of planar Sets avoiding Unit Distances
by: Ruhland, Helmut
Published: (2024)
by: Ruhland, Helmut
Published: (2024)
A new upper bound for mutually touching infinite cylinders
by: Koizumi, Junnosuke
Published: (2025)
by: Koizumi, Junnosuke
Published: (2025)
On the uniqueness of collections of pennies and marbles
by: Dewar, Sean, et al.
Published: (2023)
by: Dewar, Sean, et al.
Published: (2023)
Covering spiky annuli by planks
by: Ambrus, Gergely, et al.
Published: (2025)
by: Ambrus, Gergely, et al.
Published: (2025)
Optimal Horoball Packing Densities for Koszul-type tilings in Hyperbolic $3$-space
by: Kozma, Robert T., et al.
Published: (2022)
by: Kozma, Robert T., et al.
Published: (2022)
A note on the affine-invariant plank problem
by: Chambers, Gregory R., et al.
Published: (2016)
by: Chambers, Gregory R., et al.
Published: (2016)
On the multiplicity of arrangements of congruent zones on the sphere
by: Bezdek, A., et al.
Published: (2017)
by: Bezdek, A., et al.
Published: (2017)
On separability in discrete geometry
by: Bezdek, Károly, et al.
Published: (2024)
by: Bezdek, Károly, et al.
Published: (2024)
The density of planar sets avoiding unit distances
by: Ambrus, Gergely, et al.
Published: (2022)
by: Ambrus, Gergely, et al.
Published: (2022)
The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method
by: Lian, Yanlu, et al.
Published: (2024)
by: Lian, Yanlu, et al.
Published: (2024)
Plank theorems and their applications: a survey
by: Verreault, William
Published: (2022)
by: Verreault, William
Published: (2022)
At most 10 cylinders mutually touch: a Ramsey-theoretic approach
by: Dillon, Travis, et al.
Published: (2025)
by: Dillon, Travis, et al.
Published: (2025)
Convex bodies of constant width with exponential illumination number
by: Arman, Andrii, et al.
Published: (2023)
by: Arman, Andrii, et al.
Published: (2023)
A note on the Erdős conjecture about square packing
by: Baek, Jineon, et al.
Published: (2024)
by: Baek, Jineon, et al.
Published: (2024)
Minimal and Maximal Distances in Metric Spaces
by: Ranđelović, Žarko
Published: (2024)
by: Ranđelović, Žarko
Published: (2024)
On the general no-three-in-line problem
by: Agama, Theophilus
Published: (2021)
by: Agama, Theophilus
Published: (2021)
Borsuk and Vázsonyi problems through Reuleaux polyhedra
by: Lopez-Campos, Gyivan, et al.
Published: (2023)
by: Lopez-Campos, Gyivan, et al.
Published: (2023)
An improved lower bound to Erdos' problem concerning products of distances for fixed diameter
by: Sothanaphan, Nat
Published: (2025)
by: Sothanaphan, Nat
Published: (2025)
Energy bounds for weighted spherical codes and designs via linear programming
by: Borodachov, Sergiy, et al.
Published: (2024)
by: Borodachov, Sergiy, et al.
Published: (2024)
On the kissing number of the cross-polytope
by: Miller, Niklas
Published: (2025)
by: Miller, Niklas
Published: (2025)
Illumination number of 3-dimensional cap bodies
by: Arman, Andrii, et al.
Published: (2025)
by: Arman, Andrii, et al.
Published: (2025)
New lower bound for the optimal congruent geodesic ball packing density of screw motion groups in $\mathbf{H}^2\!\times\!\mathbf{R}$ space
by: Yahya, Arnasli, et al.
Published: (2024)
by: Yahya, Arnasli, et al.
Published: (2024)
On Hadwiger's covering problem in small dimensions
by: Arman, Andrii, et al.
Published: (2024)
by: Arman, Andrii, et al.
Published: (2024)
Power with Respect to Generalized Spheres and Radical Surfaces in $\mathbf{H}^n$
by: Világi, Áron, et al.
Published: (2026)
by: Világi, Áron, et al.
Published: (2026)
Vertex generated polytopes
by: Artstein-Avidan, Shiri, et al.
Published: (2024)
by: Artstein-Avidan, Shiri, et al.
Published: (2024)
A note on the affine plank conjecture
by: Bakaev, Egor, et al.
Published: (2026)
by: Bakaev, Egor, et al.
Published: (2026)
General penny graphs are at most 43/18-dense
by: Sagdeev, Arsenii
Published: (2024)
by: Sagdeev, Arsenii
Published: (2024)
Spherical coverings and X-raying convex bodies of constant width
by: Bondarenko, A., et al.
Published: (2020)
by: Bondarenko, A., et al.
Published: (2020)
Improved estimates on the number of unit perimeter triangles
by: Goenka, Ritesh, et al.
Published: (2023)
by: Goenka, Ritesh, et al.
Published: (2023)
Minimal dispersion on the sphere
by: Litvak, Alexander E., et al.
Published: (2025)
by: Litvak, Alexander E., et al.
Published: (2025)
A note on Borsuk's problem in Minkowski spaces
by: Raigorodskii, Andrei M., et al.
Published: (2023)
by: Raigorodskii, Andrei M., et al.
Published: (2023)
Rigidity of Koebe Polyhedra and Inversive Distance Circle Packings
by: Bowers, John C., et al.
Published: (2026)
by: Bowers, John C., et al.
Published: (2026)
Homothetic packings of centrally symmetric convex bodies
by: Dewar, Sean
Published: (2020)
by: Dewar, Sean
Published: (2020)
The chromatic number of the plane with an interval of forbidden distances is at least 7
by: Voronov, Vsevolod
Published: (2023)
by: Voronov, Vsevolod
Published: (2023)
Hadwiger's conjecture for cap bodies
by: Arman, Andrii, et al.
Published: (2025)
by: Arman, Andrii, et al.
Published: (2025)
Erdős's diameter conjecture for separated distances fails in high dimensions
by: Ho, Boon Suan
Published: (2026)
by: Ho, Boon Suan
Published: (2026)
Penny graphs in the hyperbolic plane
by: Sagmeister, Ádám, et al.
Published: (2025)
by: Sagmeister, Ádám, et al.
Published: (2025)
Similar Items
-
On lower bounds of the density of planar periodic sets without unit distances
by: Tolmachev, Alexander
Published: (2024) -
Lower Bound on Translative Covering Density of Tetrahedra
by: Li, Yiming, et al.
Published: (2022) -
Decomposition method and upper bound density related to congruent saturated hyperball packings in hyperbolic $n-$space
by: Yahya, Arnasli, et al.
Published: (2025) -
No new lower bound for the density of planar Sets avoiding Unit Distances
by: Ruhland, Helmut
Published: (2024) -
A new upper bound for mutually touching infinite cylinders
by: Koizumi, Junnosuke
Published: (2025)