10 citations · 21 across the 16 of their papers we have counts for
22 papers
The number of edges of a symmetric edge polytope
Giulia Codenotti, Roberto Riccardi, Lorenzo Venturello
The symmetric edge polytope of a simple graph is a lattice polytope defined as the convex hull of a subset of the type A roots corresponding to the edges of the graph. In this arti…
The -index of semi-Eulerian posets
Martina Juhnke-Kubitzke, José Alejandro Samper, Lorenzo Venturello
We generalize the definition of the -index of an Eulerian poset to the class of semi-Eulerian posets. For simplicial semi-Eulerian Buchsbaum posets, we show that all coefficien…
Characteristic polynomials and eigenvalues of tensors
Francesco Galuppi, Fulvio Gesmundo, Ettore Teixeira Turatti +1
We lay the geometric foundations for the study of the characteristic polynomial of tensors. For symmetric tensors of order and dimension and symmetric tensors of ord…
Triangulations of cosmological polytopes
Martina Juhnke-Kubitzke, Liam Solus, Lorenzo Venturello
A cosmological polytope is defined for a given Feynman diagram, and its canonical form may be used to compute the contribution of the Feynman diagram to the wavefunction of certain…
Voronoi diagrams of algebraic varieties under polyhedral norms
Adrian Becedas, Kathlén Kohn, Lorenzo Venturello
We study Voronoi diagrams of manifolds and varieties with respect to polyhedral norms. We provide upper and lower bounds on the dimensions of Voronoi cells. For algebraic varieties…
Equations of tensor eigenschemes
Valentina Beorchia, Francesco Galuppi, Lorenzo Venturello
We study schemes of tensor eigenvectors from an algebraic and geometric viewpoint. We characterize determinantal defining equations of such eigenschemes via linear equations in the…
On flag spheres with few equators
Lorenzo Venturello
In this note we construct a flag simplicial -sphere with the following properties: - is not a suspension; - has no edge that can be contracted to obtain another flag…
On the gamma-vector of symmetric edge polytopes
Alessio D'Alì, Martina Juhnke-Kubitzke, Daniel Köhne +1
We study -vectors associated with -vectors of symmetric edge polytopes both from a deterministic and a probabilistic point of view. On the deterministic side, we prove nonn…
The leading coefficient of Lascoux polynomials
Alessio Borzí, Xiangying Chen, Harshit J. Motwani +2
Lascoux polynomials have been recently introduced to prove polynomiality of the maximum-likelihood degree of linear concentration models. We find the leading coefficient of the Las…
Koszul Gorenstein algebras from Cohen-Macaulay simplicial complexes
Alessio D'Alì, Lorenzo Venturello
We associate with every pure flag simplicial complex a standard graded Gorenstein -algebra whose homological features are largely dictated by the combinatoric…
Spectral theory of weighted hypergraphs via tensors
Francesco Galuppi, Raffaella Mulas, Lorenzo Venturello
One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this…
Nonlinear Algebra and Applications
Paul Breiding, Türkü Özlüm Çelik, Timothy Duff +5
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, a…
Eigenschemes of Ternary Tensors
Valentina Beorchia, Francesco Galuppi, Lorenzo Venturello
We study projective schemes arising from eigenvectors of tensors, called eigenschemes. After some general results, we give a birational description of the variety parametrizing eig…
Minimality of tensors of fixed multilinear rank
Alexander Heaton, Khazhgali Kozhasov, Lorenzo Venturello
We discover a geometric property of the space of tensors of fixed multilinear (Tucker) rank. Namely, it is shown that real tensors of fixed multilinear rank form a minimal submanif…
Wasserstein Distance to Independence Models
Türkü Özlüm Çelik, Asgar Jamneshan, Guido Montúfar +2
An independence model for discrete random variables is a Segre-Veronese variety in a probability simplex. Any metric on the set of joint states of the random variables induces a Wa…
A new family of triangulations of
Lorenzo Venturello, Hailun Zheng
We construct a family of PL triangulations of the -dimensional real projective space on vertices for every . This impr…
Optimal Transport to a Variety
T. Ö. Çelik, A. Jamneshan, G. Montúfar +2
We study the problem of minimizing the Wasserstein distance between a probability distribution and an algebraic variety. We consider the setting of finite state spaces and describe…
Octahedralizing 3-colorable 3-polytopes
Giulia Codenotti, Lorenzo Venturello
We investigate the question of whether any -colorable simplicial -polytope can be octahedralized, i.e., it can be subdivided to a -dimensional geometric cross-polytopal co…
Graded Betti numbers of balanced simplicial complexes
Martina Juhnke-Kubitzke, Lorenzo Venturello
We prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for Cohen-Macaulay graded rings , wh…
Balanced triangulations on few vertices and an implementation of cross-flips
Lorenzo Venturello
A -dimensional simplicial complex is balanced if the underlying graph is -colorable. We present an implementation of cross-flips, a set of local moves introduced by Izmes…
Balanced shellings and moves on balanced manifolds
Martina Juhnke-Kubitzke, Lorenzo Venturello
A classical result by Pachner states that two -dimensional combinatorial manifolds with boundary are PL homeomorphic if and only they can be connected by a sequence of shellings…
A balanced non-partitionable Cohen-Macaulay complex
Martina Juhnke-Kubitzke, Lorenzo Venturello
In a recent paper, Duval, Goeckner, Klivans and Martin disproved the longstanding conjecture by Stanley, that every Cohen-Macaulay simplicial complex is partitionable. We construct…