Helly type problems in convexity spaces
AF Holmsen - arXiv preprint arXiv:2408.05871, 2024 - arxiv.org
We report on some recent progress regarding combinatorial properties in convexity spaces
with a bounded Radon number. In particular, we discuss the relationship between the …
with a bounded Radon number. In particular, we discuss the relationship between the …
Variations on a theme of empty polytopes
S Arun, T Dillon - arXiv preprint arXiv:2409.07262, 2024 - arxiv.org
Given a set $ S\subseteq\mathbb {R}^ d $, an empty polytope has vertices in $ S $ but
contains no other point of $ S $. Empty polytopes are closely related to so-called Helly …
contains no other point of $ S $. Empty polytopes are closely related to so-called Helly …
The prime grid contains arbitrarily large empty polygons
T Dillon - arXiv preprint arXiv:2411.10549, 2024 - arxiv.org
This paper proves a 2017 conjecture of De Loera, La Haye, Oliveros, and Rold\'an-Pensado
that the" prime grid" $\big\{(p, q)\in\mathbb {Z}^ 2:\text {$ p $ and $ q $ are …
that the" prime grid" $\big\{(p, q)\in\mathbb {Z}^ 2:\text {$ p $ and $ q $ are …