Pith. sign in

REVIEW 1 cited by

Helly-type theorems for monotone properties of boxes

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2503.22571 v1 pith:U7EBWPCN submitted 2025-03-28 math.CO

Nóra Frankl , Attila Jung This is my paper · ORCID
classification math.CO
keywords monotonepropertiesboxeshelly-typeresultstheoremsapproachcontaining
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We present a unified approach to prove Helly-type theorems for monotone properties of boxes, such as having large volume or containing points from a given set. As a corollary, we obtain new proofs for several earlier results regarding specific monotone properties. Our results generalise to $H$-convex sets as well.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Strong invariants and Tverberg numbers in convexity spaces

    math.CO 2026-07 accept novelty 7.0 of 10

    In convexity spaces, VC-dimension, strong Helly, strong Carathéodory, comatching, and strong Radon numbers coincide; for S3-separable spaces the Tverberg number satisfies r_t = O(r^2 log r) t.

Pith tools