5 papers
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…
Asymptotic number of edge-colored regular graphs
Michael Borinsky, Chiara Meroni, Maximilian Wiesmann
We prove a formula for the asymptotic number of edge-colored regular graphs with a prescribed set of allowed vertex-incidence structures. The formula depends on specific critical p…
Combinatorics of slices of cubes
Marie-Charlotte Brandenburg, Chiara Meroni
We present a complete computational classification of the combinatorial types of hyperplane sections, or slices, of the regular cube up to dimension six. For each dimension, we det…
Semialgebraic rank-one convex hulls: 2x2 triangular matrices and beyond
Chiara Meroni, Bogdan Raita
We prove that the rank-one convex hull of finitely many triangular matrices is a semialgebraic set, defined by linear and quadratic polynomials. We present explicit con…
The Best Ways to Slice a Polytope
Marie-Charlotte Brandenburg, Jesús A. De Loera, Chiara Meroni
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane a…