Zobrazeno 1 - 10
of 33
pro vyhledávání: '"Codenotti, Giulia"'
Autor:
Bajo, Esme, Braun, Benjamin, Codenotti, Giulia, Hofscheier, Johannes, Vindas-Meléndez, Andrés R.
The local $h^*$-polynomial of a lattice polytope is an important invariant arising in Ehrhart theory. Our focus in this work is on lattice simplices presented in Hermite normal form with a single non-trivial row. We prove that when the off-diagonal e
Externí odkaz:
http://arxiv.org/abs/2309.01186
Autor:
Codenotti, Giulia, Freyer, Ansgar
The purpose of this paper is to study convex bodies $C$ for which there exists no convex body $C^\prime\subsetneq C$ of the same lattice width. Such bodies shall be called ``lattice reduced'', and they occur naturally in the study of the flatness con
Externí odkaz:
http://arxiv.org/abs/2307.09429
Given a closed, convex cone $K\subseteq \mathbb{R}^n$, a multivariate polynomial $f\in\mathbb{C}[\mathbf{z}]$ is called $K$-stable if the imaginary parts of its roots are not contained in the relative interior of $K$. If $K$ is the non-negative ortha
Externí odkaz:
http://arxiv.org/abs/2206.10913
Let $A \in \{ \mathbb{Z}, \mathbb{R} \}$ and $X \subset \mathbb{R}^d$ be a bounded set. Affine transformations given by an automorphism of $\mathbb{Z}^d$ and a translation in $A^d$ are called (affine) $A$-unimodular transformations. The image of $X$
Externí odkaz:
http://arxiv.org/abs/2110.02770
Autor:
Codenotti, Giulia, Santos, Francisco
Publikováno v:
Combinatorial Theory 3(3) (2023), #2
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 the class of Cayley sums $\text{Cay}(P,Q)$ where the normal fan of $Q$ r
Externí odkaz:
http://arxiv.org/abs/1907.12312
Publikováno v:
Discrete Applied Math. 298 (July 2021), 129-142
The second and fourth authors have conjectured that a certain hollow tetrahedron $\Delta$ of width $2+\sqrt2$ attains the maximum lattice width among all three-dimensional convex bodies. We here prove a local version of this conjecture: there is a ne
Externí odkaz:
http://arxiv.org/abs/1907.06199
Autor:
Codenotti, Giulia, Venturello, Lorenzo
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 complex. We give a positive answer in dimension $3$, with the additional
Externí odkaz:
http://arxiv.org/abs/1903.10178
Publikováno v:
Discrete Comput. Geom., 67 (2022), 65-111
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 "standard terminal simplices" and direct sums of them. We prove this conject
Externí odkaz:
http://arxiv.org/abs/1903.02866
Autor:
Codenotti, Giulia, Santos, Francisco
Publikováno v:
Proc. Amer. Math. Soc. 148(2) (2020), 835-850
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 polytopes of width larger than dimension. We also construct a hollow (non
Externí odkaz:
http://arxiv.org/abs/1812.00916
Publikováno v:
Electron. J. Combin. 27:3 (2020), P3.40
We study a variation of Bagchi and Datta's $\sigma$-vector of a simplicial complex $C$, whose entries are defined as weighted averages of Betti numbers of induced subcomplexes of $C$. We show that these invariants satisfy an Alexander-Dehn-Sommervill
Externí odkaz:
http://arxiv.org/abs/1808.04220