25 citations · 181 across the 41 of their papers we have counts for
20 papers · 1 filter
Tensors in statistics and rigidity theory
Fatemeh Mohammadi
This is a short report on the discussions of appearance of tensors in algebraic statistics and rigidity theory, during the semester ``AGATES: Algebraic Geometry with Applications t…
Double Schubert polynomials do have saturated Newton polytopes
Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi +1
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…
Multigraded algebras and multigraded linear series
Yairon Cid-Ruiz, Fatemeh Mohammadi, Leonid Monin
This paper is devoted to the study of multigraded algebras and multigraded linear series. For an -graded algebra , we define and study its volume function $F_A:\ma…
Standard monomial theory and toric degenerations of Richardson varieties in the Grassmannian
Narasimha Chary Bonala, Oliver Clarke, Fatemeh Mohammadi
Richardson varieties are obtained as intersections of Schubert and opposite Schubert varieties. We provide a new family of toric degenerations of Richardson varieties inside Grassm…
Conditional probabilities via line arrangements and point configurations
Oliver Clarke, Fatemeh Mohammadi, Harshit J. Motwani
We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a…
Standard monomial theory and toric degenerations of Schubert varieties from matching field tableaux
Oliver Clarke, Fatemeh Mohammadi
We study Gröbner degenerations of Schubert varieties inside flag varieties. We consider toric degenerations of flag varieties induced by matching fields and semi-standard Young tab…
Toric degenerations of flag varieties from matching field tableaux
Oliver Clarke, Fatemeh Mohammadi
We present families of tableaux which interpolate between the classical semi-standard Young tableaux and matching field tableaux. Algebraically, this corresponds to SAGBI bases of…
Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux
Oliver Clarke, Fatemeh Mohammadi
We study the combinatorics of Gröbner degenerations of Grassmannians and the Schubert varieties inside them. We provide a family of binomial ideals whose combinatorics is governed…
Measuring the non-Gorenstein locus of Hibi rings and normal affine semigroup rings
Jürgen Herzog, Fatemeh Mohammadi, Janet Page
The trace of the canonical module of a Cohen-Macaulay ring describes its non-Gorenstein locus. We study the trace of the canonical module of a Segre product of algebras, and we app…
Polarization and depolarization of monomial ideals with application to multistate system reliability
Fatemeh Mohammadi, Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón +1
We study the family of depolarizations of a squarefree monomial ideal , i.e. all monomial ideals whose polarization is . We describe a method to find all depolarizations of $…
Types of signature analysis in reliability based on Hilbert series
Fatemeh Mohammadi, Eduardo Sáenz-de-Cabezón, Henry P. Wynn
The present paper studies multiple failure and signature analysis of coherent systems using the theory of monomial ideals. While system reliability has been studied using Hilbert s…
On the Orlik--Terao ideal and the relation space of a hyperplane arrangement
Le Van Dinh, Fatemeh Mohammadi
The relation space of a hyperplane arrangement is the vector space of all linear dependencies among the defining forms of the hyperplanes in the arrangement. In this paper, we stud…
Cellular resolutions from mapping cones
Anton Dochtermann, Fatemeh Mohammadi
One can iteratively obtain a free resolution of any monomial ideal by considering the mapping cone of the map of complexes associated to adding one generator at a time. Herzog…
Prime splittings of Determinantal Ideals
Fatemeh Mohammadi, Johannes Rauh
We consider determinantal ideals, where the generating minors are encoded in a hypergraph. We study when the generating minors form a Gröbner basis. In this case, the ideal is radi…
Determinantal Facet Ideals
Viviana Ene, Juergen Herzog, Takayuki Hibi +1
We consider ideals generated by general sets of -minors of an -matrix of indeterminates. The generators are identified with the facets of an -dimensional pure…
Monomial ideals and toric rings of Hibi type arising from a finite poset
Viviana Ene, Juergen Herzog, Fatemeh Mohammadi
In this paper we study monomial ideals attached to posets, introduce generalized Hibi rings and investigate their algebraic and homological properties. The main tools to study thes…
Resolution of Unmixed Bipartite Graphs
Fatemeh Mohammadi, Somayeh Moradi
For an unmixed bipartite graph we consider the lattice of vertex covers and compute depth, projective dimension and extremal Betti-numbers of in terms…
Poincaré series of some hypergraph algebras
Eric Emtander, Ralf Fröberg, Fatemeh Mohammadi +1
A hypergraph , where and defines a hypergraph algebra . All our hypergr…
Some algebraic properties of hypergraphs
Eric Emtander, Fatemeh Mohammadi, Somayeh Moradi
We consider Stanley--Reisner rings $k[x_1,...,x_n]/I(\mc{H})$ where $I(\mc{H})$ is the edge ideal associated to some particular classes of hypergraphs. For instance, we consider hy…
Arithmetical rank of the cyclic and bicyclic graphs
Margherita Barile, Dariush Kiani, Fatemeh Mohammadi +1
We show that for the edge ideals of the graphs consisting of one cycle or two cycles of any length connected through a vertex or a path, the arithmetical rank equals the projective…