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Main Authors:	Baek, Jineon, Koizumi, Junnosuke, Ueoro, Takahiro
Format:	Preprint
Published:	2024
Subjects:	Combinatorics Metric Geometry 52C15, 52C10
Online Access:	https://arxiv.org/abs/2411.07274
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A new upper bound for mutually touching infinite cylinders
by: Koizumi, Junnosuke
Published: (2025)

$n^2 + 1$ unit equilateral triangles cannot cover an equilateral triangle of side $> n$ if all triangles have parallel sides
by: Baek, Jineon, et al.
Published: (2023)

Erdős's diameter conjecture for separated distances fails in high dimensions
by: Ho, Boon Suan
Published: (2026)

At most 10 cylinders mutually touch: a Ramsey-theoretic approach
by: Dillon, Travis, et al.
Published: (2025)

General penny graphs are at most 43/18-dense
by: Sagdeev, Arsenii
Published: (2024)

Isosceles trapezoids of unit area with vertices in sets of infinite planar measure
by: Koizumi, Junnosuke
Published: (2025)

An improved lower bound to Erdos' problem concerning products of distances for fixed diameter
by: Sothanaphan, Nat
Published: (2025)

Homothetic packings of centrally symmetric convex bodies
by: Dewar, Sean
Published: (2020)

On iterated circumcenter sequences
by: Kanda, Shuho, et al.
Published: (2024)

Minimal and Maximal Distances in Metric Spaces
by: Ranđelović, Žarko
Published: (2024)

On the general no-three-in-line problem
by: Agama, Theophilus
Published: (2021)

A Conditional Upper Bound for the Moving Sofa Problem
by: Baek, Jineon
Published: (2024)

On Distinct Angles in the Plane
by: Konyagin, Sergei V., et al.
Published: (2024)

Penny graphs in the hyperbolic plane
by: Sagmeister, Ádám, et al.
Published: (2025)

Nearly equal distances in the plane, II
by: Erdős, P., et al.
Published: (2021)

Monochromatic infinite sets in Minkowski planes
by: Frankl, Nóra, et al.
Published: (2023)

On the Erdős distance problem
by: Agama, Theophilus
Published: (2020)

Magnitude homology of real hyperplane arrangements
by: Koizumi, Junnosuke, et al.
Published: (2026)

No new lower bound for the density of planar Sets avoiding Unit Distances
by: Ruhland, Helmut
Published: (2024)

Decomposition method and upper bound density related to congruent saturated hyperball packings in hyperbolic $n-$space
by: Yahya, Arnasli, et al.
Published: (2025)

On the uniqueness of collections of pennies and marbles
by: Dewar, Sean, et al.
Published: (2023)

Empty simplices of large width
by: Doolittle, Joseph, et al.
Published: (2021)

Borsuk and Vázsonyi problems through Reuleaux polyhedra
by: Lopez-Campos, Gyivan, et al.
Published: (2023)

Generalised rigid body motions in non-Euclidean planes with applications to global rigidity
by: Dewar, Sean, et al.
Published: (2021)

Improved estimates on the number of unit perimeter triangles
by: Goenka, Ritesh, et al.
Published: (2023)

Angular constraints on planar frameworks
by: Dewar, Sean, et al.
Published: (2024)

On lower bounds of the density of planar periodic sets without unit distances
by: Tolmachev, Alexander
Published: (2024)

Rigidity of Circle Packings with Flexible Radii
by: Connelly, Robert, et al.
Published: (2022)

Families of lattices with an unbounded number of unit vectors
by: Ruhland, Helmut
Published: (2024)

Canonical Ramsey: triangles, rectangles and beyond
by: Fang, Yijia, et al.
Published: (2025)

Visibility cliques, cubic containers, and dense orchard cores
by: Sarkar, Sohail
Published: (2026)

A note on Borsuk's problem in Minkowski spaces
by: Raigorodskii, Andrei M., et al.
Published: (2023)

Identifying contact graphs of sphere packings with generic radii
by: Dewar, Sean
Published: (2023)

On the maximum product of distances of diameter $2$ point sets
by: Cambie, Stijn, et al.
Published: (2026)

More unit distances in arbitrary norms
by: Greilhuber, Josef, et al.
Published: (2024)

Edge-length preserving embeddings of graphs between normed spaces
by: Dewar, Sean, et al.
Published: (2024)

Uniquely realisable graphs in polyhedral normed spaces
by: Dewar, Sean
Published: (2025)

Reducing the upper bound for the Borsuk number in $\mathbb{R}^4$ to 8
by: Tolmachev, Alexander, et al.
Published: (2026)

Regular matchstick graphs on the sphere
by: Swanepoel, Konrad J.
Published: (2025)

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// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

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