Hailun Zheng

activity

20242026

collaborators

7 papers

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

Transversal numbers of simplicial polytopes, spheres, and pure complexes

Isabella Novik, Hailun Zheng

We prove new upper and lower bounds on transversal numbers of several classes of simplicial complexes. Specifically, we establish an upper bound on the transversal numbers of pure…

math.CO2025

Missing faces of neighborly and nearly neighborly polytopes and spheres

Isabella Novik, Hailun Zheng

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

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

Transversal numbers of simplicial polytopes, spheres, and pure complexes

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 $g_{k} = 1$