18 citations · 42 across the 18 of their papers we have counts for
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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…
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…
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…
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…