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math.CO2026
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…
math.CO2026
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…
math.AC2026
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…