Giulia Codenotti

activity

20172022

most citedHollow polytopes of large width

9 citations · 22 across the 7 of their papers we have counts for

collaborators

9 papers

math.CO2022

Combinatorics and preservation of conically stable polynomials

Giulia Codenotti, Stephan Gardoll, Thorsten Theobald

Given a closed, convex cone $K \subseteq R^{n}$ , a multivariate polynomial $f \in C [z]$ is called $K$ -stable if the imaginary parts of its roots are not conta…

math.MG2021

Generalised Flatness Constants: A Framework Applied in Dimension $2$

Giulia Codenotti, Thomas Hall, Johannes Hofscheier

Let $A \in {Z, R}$ and $X \subset R^{d}$ be a bounded set. Affine transformations given by an automorphism of $Z^{d}$ and a translation in $A^{d}$ …

math.CO2019

Unimodular covers of 3-dimensional parallelepipeds and Cayley sums

Giulia Codenotti, Francisco Santos

We show that the following classes of lattice polytopes have unimodular covers, in dimension three: the class of parallelepipeds, the class of centrally symmetric polytopes, and th…

math.CO2019★ 6 cited

A local maximizer for lattice width of $3$ -dimensional hollow bodies

Gennadiy Averkov, Giulia Codenotti, Antonio Macchia +1

The second and fourth authors have conjectured that a certain hollow tetrahedron $Δ$ of width $2 + 2$ attains the maximum lattice width among all three-dimensional convex bodies…

math.CO2019

Octahedralizing 3-colorable 3-polytopes

Giulia Codenotti, Lorenzo Venturello

We investigate the question of whether any $d$ -colorable simplicial $d$ -polytope can be octahedralized, i.e., it can be subdivided to a $d$ -dimensional geometric cross-polytopal co…

math.CO2019★ 3 cited

The covering radius and a discrete surface area for non-hollow simplices

Giulia Codenotti, Francisco Santos, Matthias Schymura

We explore upper bounds on the covering radius of non-hollow lattice polytopes. In particular, we conjecture a general upper bound of $d /2$ in dimension $d$ , achieved by the "stand…

math.CO2018★ 9 cited

Hollow polytopes of large width

Giulia Codenotti, Francisco Santos

We construct a hollow lattice polytope (resp. a hollow lattice simplex) of dimension $14$ (resp. $404$ ) and of width $15$ (resp. $408$ ). They are the first known hollow lattice pol…

math.CO2018★ 2 cited

Average Betti numbers of induced subcomplexes in triangulations of manifolds

Giulia Codenotti, Francisco Santos, Jonathan Spreer

We study a variation of Bagchi and Datta's $σ$ -vector of a simplicial complex $C$ , whose entries are defined as weighted averages of Betti numbers of induced subcomplexes of $C$ . W…

math.CO2017★ 2 cited

On f- and h- vectors of relative simplicial complexes

Giulia Codenotti, Lukas Katthän, Raman Sanyal

A relative simplicial complex is a collection of sets of the form $Δ ∖ Γ$ , where $Γ \subset Δ$ are simplicial complexes. Relative complexes played key roles in recent advance…