Isabella Novik

activity

20242026

collaborators

4 papers

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.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…

math.CO2024

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…

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

Simplicial spheres with gk​=1

Missing faces of neighborly and nearly neighborly polytopes and spheres

Transversal numbers of simplicial polytopes, spheres, and pure complexes

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

Simplicial spheres with $g_{k} = 1$