English
norskBlar i forfatter "Mohammadi, Fatemeh"
Viser treff 1-4 av 4
-
Double Schubert polynomials do have saturated Newton polytopes
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-11-03)We prove that double Schubert polynomials have the saturated Newton polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory of multidegrees. We introduce a notion of standardization of ideals that enables us to study nonstandard multigradings. This allows us to show that the support of the multidegree polynomial of each Cohen–Macaulay prime ... -
Families of Gröbner Degenerations, Grassmannians and Universal Cluster Algebras
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-06-10)Let V be the weighted projective variety defined by a weighted homogeneous ideal J and C a maximal cone in the Gröbner fan of J with m rays. We construct a flat family over A<sup>m</sup> that assembles the Gröbner degenerations of V associated with all faces of C. This is a multi-parameter generalization of the classical one-parameter Gröbner degeneration associated to a weight. We explain how our ... -
Lattice conditional independence models and Hibi ideals
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-06-10)Lattice conditional independence models [Andersson and Perlman, Lattice models for conditional independence in a multivariate normal distribution, Ann. Statist. 21 (1993), 1318–1358] are a class of models developed first for the Gaussian case in which a distributive lattice classifies all the conditional independence statements. The main result is that these models can equivalently be described via ... -
Matroid Stratifications of Hypergraph Varieties, Their Realization Spaces, and Discrete Conditional Independence Models
(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-11-01)We study varieties associated to hypergraphs from the point of view of projective geometry and matroid theory. We describe their decompositions into matroid varieties, which may be reducible and can have arbitrary singularities by the Mnëv–Sturmfels universality theorem. We focus on various families of hypergraph varieties for which we explicitly compute an irredundant irreducible decomposition. Our ...
