3 papers
math.CO2026
Integer decomposition property of three-dimensional smooth polytopes: a shorter proof
Juliana Curtis, Gaku Liu
Oda's smoothness conjecture asserts that every smooth lattice polytope has the integer decomposition property. The three-dimensional case of this conjecture was recently proven by…
math.CO2026
Reconstruction of slices of cubes
Marie-Charlotte Brandenburg, Juliana Curtis, Chiara Giardino +2
We prove that the combinatorial type of a slice of the cube by a hyperplane is completely determined by its graph, within the class of cube slices. We also show that such a result…
math.CO2026
On Smooth Combinatorial Products of Simplices
Juliana Curtis, Tuong Le, Chayim Lowen
We show that every lattice weak Minkowski summand of a smooth polytope combinatorially isomorphic to a product of simplices has a quadratic triangulation. This is achieved by ident…