Hailun Zheng

activity

20182026

most citedA new valuation on polyhedral cones

1 citations · 1 across the 6 of their papers we have counts for

collaborators

15 papers

math.CO2026

On Unavoidable Faces of High-Dimensional Polytopes

Jesús A. De Loera, Ethan X. Fang, Shengtao Guo +2

Kalai's cube--simplex conjecture asserts that for all positive integers $ℓ, k$ , there is an integer $f (ℓ, k)$ such that every polytope of dimension at least $f (ℓ, k)$ has eit…

math.CO2026

Sharp Bounds on the Independence Number of Simplicial Spheres

Jesús A. De Loera, Ethan X. Fang, Junwei Lu +2

We study the maximum size of an independent set in the graph of a simplicial sphere. Let $β (d, n)$ denote this maximum over all simplicial $(d - 1)$ -spheres on $n$ vertices, and let $…

math.CO2026

Lower bounds on the $g$ -numbers of spheres without large missing faces

Isabella Novik, Hailun Zheng

We establish several new lower bounds on the $g$ -numbers of simplicial spheres without large missing faces. For this class of spheres, we derive bounds on the $g$ -numbers in terms…

math.CO2026

Simplicial spheres with $g_{k} = 1$

Isabella Novik, Hailun Zheng

For $d \geq 4$ , Kalai (1987) characterized all simplicial $(d - 1)$ -spheres with $g_{2} = 0$ , and for $k \geq 2$ and $d \geq 2 k$ , Murai and Nevo (2013) characterized all simplicial $(d - 1)$ -…

math.AG2025

The geometric Merkurjev-Panin Conjecture for the Cox category

Daniel Erman, Andrew Hanlon, Gaku Liu +1

We show that a strong version of the geometric Merkurjev-Panin conjecture holds for the Cox category of a projective toric variety. That is, we prove that the full strong exception…

math.CO2025

Missing faces of neighborly and nearly neighborly polytopes and spheres

Isabella Novik, Hailun Zheng

For a $(d - 1)$ -dimensional simplicial complex $Δ$ and $1 \leq i \leq d$ , let $f_{i - 1}$ be the number of $(i - 1)$ -faces of $Δ$ and $m_{i}$ be the number of missing $i$ -faces of $Δ$ . In th…

On Unavoidable Faces of High-Dimensional Polytopes

Sharp Bounds on the Independence Number of Simplicial Spheres

Lower bounds on the g-numbers of spheres without large missing faces

Simplicial spheres with gk​=1

The geometric Merkurjev-Panin Conjecture for the Cox category

Missing faces of neighborly and nearly neighborly polytopes and spheres

Lower bounds on the $g$ -numbers of spheres without large missing faces

Simplicial spheres with $g_{k} = 1$