Cover Image

A geometric proof of the infinite $(p, q)$-theorem for hyperplane piercing

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Chakraborty, Sutanoya, Ghosh, Arijit, Nandi, Soumi
Format:	Preprint
Published:	2024
Subjects:	Combinatorics Computational Geometry 52A35
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Helly theorem for affine spaces without dimensions
by: Chakraborty, Sutanoya, et al.
Published: (2023)

Colorful two-piercing theorem for boxes
by: Chakraborty, Sourav, et al.
Published: (2022)

Stabbing boxes with finitely many axis-parallel lines and flats
by: Chakraborty, Sutanoya, et al.
Published: (2023)

Finite k-Transversals of Infinite Families of Fat Convex Sets
by: Chakraborty, Sutanoya, et al.
Published: (2022)

Largest dyadic dual VC-dimension of non-piercing families
by: Huang, Xinqi, et al.
Published: (2025)

No Infinite $(p,q)$-Theorem for Piercing Compact Convex Sets with Lines in $\mathbb{R}^3$
by: Chakraborty, Sutanoya, et al.
Published: (2025)

A note on infinite versions of $(p,q)$-theorems
by: Jung, Attila, et al.
Published: (2024)

A complex analogue of the Goodman-Pollack-Wenger theorem
by: McGinnis, Daniel
Published: (2023)

$k$-dimensional transversals for fat convex sets
by: Jung, Attila, et al.
Published: (2023)

An $(\aleph_0,k+2)$-Theorem for $k$-Transversals
by: Keller, Chaya, et al.
Published: (2023)

Addition theorems for Ziegler pairs of hyperplane arrangements
by: Abe, Takuro, et al.
Published: (2025)

Bisecting masses with families of parallel hyperplanes
by: Hubard, Alfredo, et al.
Published: (2024)

A necessary and sufficient condition for $k$-transversals
by: McGinnis, Daniel, et al.
Published: (2024)

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

Colorful positive bases decomposition and Helly-type results for cones
by: Ivanov, Grigory
Published: (2024)

Generalized angle vectors, geometric lattices, and flag-angles
by: Backman, Spencer, et al.
Published: (2018)

An elementary proof of Sierksma's conjecture for seven points in the plane
by: Soberón, Pablo
Published: (2026)

An example of an "unlinked" set of $2k + 3$ points in $2k$-space
by: Starkov, M.
Published: (2024)

Extensions of discrete Helly theorems for boxes
by: Edwards, Timothy, et al.
Published: (2024)

Helly-type theorems for monotone properties of boxes
by: Frankl, Nóra, et al.
Published: (2025)

Stable hyperplane arrangements
by: Oshima, Toshio
Published: (2025)

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

Topological Drawings meet Classical Theorems from Convex Geometry
by: Bergold, Helena, et al.
Published: (2020)

A hyperplane Ham Sandwich theorem
by: Crabb, M. C.
Published: (2024)

On colorful generalizations of the Goodman--Pollack transversal problem
by: Sadovek, Nikola
Published: (2026)

New Sufficient Conditions for Linear-Sized Epsilon-Nets and $(p,2)$-Theorems
by: Keller, Chaya, et al.
Published: (2025)

Quantitative Steinitz theorem and polarity
by: Ivanov, Grigory
Published: (2024)

From spherical separation center set to the upper and lower bound theorems
by: Han, Huhe
Published: (2024)

Convex bodies of constant width with exponential illumination number
by: Arman, Andrii, et al.
Published: (2023)

When Grünbaum meets Poncelet -- Infinite Classes of Movable $n_4$ Configurations
by: Berman, Leah Wrenn, et al.
Published: (2024)

Explicit Constructions for Poncelet Polygons
by: Berman, Leah Wrenn, et al.
Published: (2024)

Strata of toric hyperplane arrangements, zonotope lattice points, and the Bondal-Thomsen collection
by: Bauermeister, Friedrich, et al.
Published: (2025)

Short proofs of Tverberg-type theorems for cell complexes
by: Karasev, Roman, et al.
Published: (2024)

On Lines Crossing Pairwise Intersecting Convex Sets in Three Dimensions
by: Rubin, Natan
Published: (2026)

Intersection Bodies of Polytopes: Translations and Convexity
by: Brandenburg, Marie-Charlotte, et al.
Published: (2023)

Bisections of mass assignments by parallel hyperplanes
by: Sadovek, Nikola, et al.
Published: (2025)

Region level via centralization for hyperplane arrangements and beyond
by: Southerland, Finn, et al.
Published: (2025)

The Discrete Gauss Image Problem
by: Semenov, Vadim
Published: (2022)

Indecomposability of the median hypersimplex and polytopality of the hemi-icosahedral Bier sphere
by: Jevtić, Filip D., et al.
Published: (2025)

Convex Geometry of Building Sets
by: Backman, Spencer, et al.
Published: (2024)