I. Novik

activity

20002023

most citedLower Bound Theorems and a Generalized Lower Bound Conjecture for balanced simplicial complexes

19 citations · 94 across the 40 of their papers we have counts for

collaborators

44 papers

math.CO2023

Affine stresses, inverse systems, and reconstruction problems

Satoshi Murai, Isabella Novik, Hailun Zheng

A conjecture of Kalai asserts that for $d \geq 4$ , the affine type of a prime simplicial $d$ -polytope $P$ can be reconstructed from the space of affine $2$ -stresses of $P$ . We prove…

math.CO2023

The merging operation and $(d - i)$ -simplicial $i$ -simple $d$ -polytopes

Isabella Novik, Hailun Zheng

We define a certain merging operation that given two $d$ -polytopes $P$ and $Q$ such that $P$ has a simplex facet $F$ and $Q$ has a simple vertex $v$ produces a new $d$ -polytope $P\…

math.CO2022

Neighborly spheres and transversal numbers

Isabella Novik, Hailun Zheng

We survey several old and new problems related to the number of simplicial spheres, the number of neighborly simplicial spheres, the number of centrally symmetric simplicial sphere…

math.CO2022★ 2 cited

Affine stresses: the partition of unity and Kalai's reconstruction conjectures

Isabella Novik, Hailun Zheng

Kalai conjectured that if $P$ is a simplicial $d$ -polytope that has no missing faces of dimension $d - 1$ , then the graph of $P$ and the space of affine $2$ -stresses of $P$ determine…

math.CO2021

Reconstructing simplicial polytopes from their graphs and affine $2$ -stresses

Isabella Novik, Hailun Zheng

A conjecture of Kalai from 1994 posits that for an arbitrary $2 \leq k \leq ⌊ d /2 ⌋$ , the combinatorial type of a simplicial $d$ -polytope $P$ is uniquely determined by th…

math.CO2021

Many neighborly spheres

Isabella Novik, Hailun Zheng

The result of Padrol asserts that for every $d \geq 4$ , there exist $2^{Ω (n l o g n)}$ distinct combinatorial types of $⌊ d /2 ⌋$ -neighborly simplicial $(d - 1)$ -spheres with…

Affine stresses, inverse systems, and reconstruction problems

The merging operation and (d−i)-simplicial i-simple d-polytopes

Neighborly spheres and transversal numbers

Affine stresses: the partition of unity and Kalai's reconstruction conjectures

Reconstructing simplicial polytopes from their graphs and affine 2-stresses

Many neighborly spheres

The merging operation and $(d - i)$ -simplicial $i$ -simple $d$ -polytopes

Reconstructing simplicial polytopes from their graphs and affine $2$ -stresses