21 citations · 100 across the 15 of their papers we have counts for
7 papers · 1 filter
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…
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…