21 citations · 100 across the 15 of their papers we have counts for
16 papers
On strongly Koszul algebras and tidy Gröbner bases
Alessio D'Alì
Strongly Koszul algebras were introduced by Herzog, Hibi and Restuccia in 2000. The goal of the present paper is to provide an in-depth study of such algebras and to investigate ho…
Order polytopes of graded posets are gamma-effective
Alessio D'Alì, Akihiro Higashitani
Order polytopes of posets have been a very rich topic at the crossroads between combinatorics and discrete geometry since their definition by Stanley in 1986. Among other notable r…
Equivariant Hilbert and Ehrhart series under translative group actions
Alessio D'Alì, Emanuele Delucchi
We study representations of finite groups on Stanley--Reisner rings of simplicial complexes and on lattice points in lattice polytopes. The framework of translative group actions a…
On a generalization of symmetric edge polytopes to regular matroids
Alessio D'Alì, Martina Juhnke-Kubitzke, Melissa Koch
Starting from any finite simple graph, one can build a reflexive polytope known as a symmetric edge polytope. The first goal of this paper is to show that symmetric edge polytopes…
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…
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…
Graded algebras with cyclotomic Hilbert series
Alessio Borzì, Alessio D'Alì
Let be a positively graded algebra over a field. We say that is Hilbert-cyclotomic if the numerator of its reduced Hilbert series has all of its roots on the unit circle. S…
Many faces of symmetric edge polytopes
Alessio D'Alì, Emanuele Delucchi, Mateusz Michałek
Symmetric edge polytopes are a class of lattice polytopes constructed from finite simple graphs. In the present paper we highlight their connections to the Kuramoto synchronization…
Stanley-Reisner rings for symmetric simplicial complexes, G-semimatroids and Abelian arrangements
Alessio D'Alì, Emanuele Delucchi
We extend the notion of face rings of simplicial complexes and simplicial posets to the case of finite-length (possibly infinite) simplicial posets with a group action. The action…
The Geometry of Gaussoids
Tobias Boege, Alessio D'Alì, Thomas Kahle +1
A gaussoid is a combinatorial structure that encodes independence in probability and statistics, just like matroids encode independence in linear algebra. The gaussoid axioms of Ln…
The Koszul property for spaces of quadrics of codimension three
Alessio D'Alì
In this paper we prove that, if is an algebraically closed field of characteristic different from 2, almost all quadratic standard graded -algebras suc…
Resolutions of letterplace ideals of posets
Alessio D'Alì, Gunnar Fløystad, Amin Nematbakhsh
We investigate resolutions of letterplace ideals of posets. We develop topological results to compute their multigraded Betti numbers, and to give structural results on these Betti…
Resolutions of co-letterplace ideals and generalizations of Bier spheres
Alessio D'Alì, Gunnar Fløystad, Amin Nematbakhsh
We give the resolutions of co-letterplace ideals of posets in a completely explicit, very simple form. This generalizes and simplifies a number of linear resolutions in the literat…
Edge ideals and DG algebra resolutions
Adam Boocher, Alessio D'Alì, Eloísa Grifo +2
Let where and is a homogeneous ideal in . The acyclic closure of over is a DG algebra resolution obtained by…
On the growth of deviations
Adam Boocher, Alessio D'Alì, Eloísa Grifo +2
The deviations of a graded algebra are a sequence of integers that determine the Poincare series of its residue field and arise as the number of generators of certain DG algebras.…
Toric ideals associated with gap-free graphs
Alessio D'Alì
In this article we prove that every toric ideal associated with a gap-free graph has a squarefree lexicographic initial ideal. Moreover, in the particular case when the complem…