18 citations · 42 across the 18 of their papers we have counts for
23 papers
The equivariant Ehrhart theory of polytopes with order-two symmetries: Part II
Oliver Clarke
We give two counterexamples to Stapledon's Effectiveness Conjecture. Each counterexample is a -dimensional lattice polytope with an order-two symmetry whose equivariant -se…
The phylogenetic rank of a graph
Franklin Ashworth, Oliver Clarke, Jeffrey Giansiracusa +3
The Pachter-Sturmfels phylogenetic rank of a graph G is the minimal number of metric trees needed to embed G isometrically. Here, all edges of G are of length one and the product o…
Distance Reduction in Bouquet Decompositions and Toric Ideals of Graphs
Oliver Clarke, Dimitra Kosta, Alexander Milner
The distance-reduction property for a generating set, i.e., a Markov basis, of a toric ideal is a condition that ensures tight connectivity of its fibres. In this paper, we study t…
Computing all minimal Markov bases in Macaulay2
Oliver Clarke, Alexander Milner
We introduce the package allMarkovBases for Macaulay2, which is used to compute all minimal Markov bases of a given toric ideal. The package builds on functionality of 4ti2 by prod…
Minimal cellular resolutions of powers of matching field ideals
Oliver Clarke, Fatemeh Mohammadi
We study a family of monomial ideals, called block diagonal matching field ideals, which arise as monomial Gröbner degenerations of determinantal ideals. Our focus is on the minima…
Liftable Point-Line Configurations: Defining Equations and Irreducibility of Associated Matroid and Circuit Varieties
Oliver Clarke, Giacomo Masiero, Fatemeh Mohammadi
We study point-line configurations through the lens of projective geometry and matroid theory. Our focus is on their realisation spaces, where we introduce the concepts of liftable…
Matching Fields in Macaulay2
Oliver Clarke
This article introduces the package MatchingFields for Macaulay2 and highlights some open problems. A matching field is a combinatorial object whose data encodes a candidate toric…
SubalgebraBases in Macaulay2
Michael Burr, Oliver Clarke, Timothy Duff +3
We describe a recently revived version of the software package SubalgberaBases, which is distributed in the Macaulay2 computer algebra system. The package allows the user to comput…
Restricted Chain-Order Polytopes via Combinatorial Mutations
Oliver Clarke, Akihiro Higashitani, Francesca Zaffalon
We study restricted chain-order polytopes associated to Young diagrams using combinatorial mutations. These polytopes are obtained by intersecting chain-order polytopes with certai…
The equivariant Ehrhart theory of polytopes with order-two symmetries
Oliver Clarke, Akihiro Higashitani, Max Kölbl
We study the equivariant Ehrhart theory of families of polytopes that are invariant under a non-trivial action of the group with order two. We study families of polytopes whose equ…
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…
Toric degenerations of partial flag varieties and combinatorial mutations of matching field polytopes
Oliver Clarke, Fatemeh Mohammadi, Francesca Zaffalon
We study toric degenerations arising from Gröbner degenerations or the tropicalization of partial flag varieties. We produce a new family of toric degenerations of partial flag var…
A study of nonlinear multiview varieties
Yairon Cid-Ruiz, Oliver Clarke, Fatemeh Mohammadi
We study the nonlinear generalization of the classical multiview variety, which is a fundamental concept in computer vision. In this paper, we take the first comprehensive step to…
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…
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…
Standard monomial theory and toric degenerations of Richardson varieties in flag varieties
Narasimha Chary Bonala, Oliver Clarke, Fatemeh Mohammadi
We study standard monomial bases for Richardson varieties inside the flag variety. In general, writing down a standard monomial basis for a Richardson variety can be challenging, a…
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…
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…
Standard monomial theory and toric degenerations of Richardson varieties inside Grassmannians and flag varieties
Narasimha Chary Bonala, Oliver Clarke, Fatemeh Mohammadi
We study toric degenerations of opposite Schubert and Richardson varieties inside degenerations of Grassmannians and flag varieties. These degenerations are parametrized by matchin…
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…
Conditional independence ideals with hidden variables
Oliver Clarke, Fatemeh Mohammadi, Johannes Rauh
We study a class of determinantal ideals that are related to conditional independence (CI) statements with hidden variables. Such CI statements correspond to determinantal conditio…