25 citations · 181 across the 41 of their papers we have counts for
12 papers · 1 filter
On the uniqueness of collections of pennies and marbles
Sean Dewar, Georg Grasegger, Kaie Kubjas +2
In this note we study the uniqueness problem for collections of pennies and marbles. More generally, consider a collection of unit -spheres that may touch but not overlap. Given…
Combinatorial Mutations of Gelfand-Tsetlin Polytopes, Feigin-Fourier-Littelmann-Vinberg Polytopes, and Block Diagonal Matching Field Polytopes
Oliver Clarke, Akihiro Higashitani, Fatemeh Mohammadi
The Gelfand-Tsetlin and the Feigin-Fourier-Littelmann-Vinberg polytopes for the Grassmannians are defined, from the perspective of representation theory, to parametrize certain bas…
Global Rigidity of Line Constrained Frameworks
James Cruickshank, Fatemeh Mohammadi, Harshit J Motwani +2
We consider the global rigidity problem for bar-joint frameworks where each vertex is constrained to lie on a particular line in . In our setting we allow multiple ver…
Computing positroid cells in the Grassmannian of lines, their boundaries and their intersections
Susama Agarwala, Fatemeh Mohammadi, Francesca Zaffalon
Positroids are families of matroids introduced by Postnikov in the study of non-negative Grassmannians. In particular, positroids enumerate a CW decomposition of the totally non-ne…
Matroid stratifications of hypergraph varieties, their realization spaces, and discrete conditional independence models
Oliver Clarke, Kevin Grace, Fatemeh Mohammadi +1
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…
Combinatorial Mutations and Block Diagonal Polytopes
Oliver Clarke, Akihiro Higashitani, Fatemeh Mohammadi
Matching fields were introduced by Sturmfels and Zelevinsky to study certain Newton polytopes and more recently have been shown to give rise to toric degenerations of various famil…
Triangulations and Canonical Forms of Amplituhedra: a fiber-based approach beyond polytopes
Fatemeh Mohammadi, Leonid Monin, Matteo Parisi
Any totally positive matrix induces a map from the positive Grassmannian to the Grassmannian , whose image is the amplituhe…
An Efficient Algorithm for Computing Network Reliability in Small Treewidth
Amir Kafshdar Goharshady, Fatemeh Mohammadi
We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edg…
The algebraic method in tree percolation
Fatemeh Mohammadi, Eduardo Sáenz-de-Cabezón, Henry P. Wynn
We apply the methods of algebraic reliability to the study of percolation on trees. To a complete -ary tree of depth we assign a monomial ideal on $\sum_…
Divisors on graphs, orientations, syzygies, and system reliability
Fatemeh Mohammadi
We study various ideals arising in the theory of system reliability. We use ideas from the theory of divisors, orientations and matroids on graphs to describe the minimal polyhedra…
Divisors on graphs, binomial and monomial ideals, and cellular resolutions
Fatemeh Mohammadi, Farbod Shokrieh
We study various binomial and monomial ideals arising in the theory of divisors, orientations, and matroids on graphs. We use ideas from potential theory on graphs and from the the…
Divisors on graphs, Connected flags, and Syzygies
Fatemeh Mohammadi, Farbod Shokrieh
We study the binomial and monomial ideals arising from linear equivalence of divisors on graphs from the point of view of Gröbner theory. We give an explicit description of a minim…