3 citations · 8 across the 13 of their papers we have counts for
13 papers · 1 filter
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…
Combinatorial slicing problems of polytopes: How (not) to reconstruct a polytope from its slices
Anna Birkemeyer, Anouk E. Brose, Marie-Charlotte Brandenburg +1
We study combinatorial aspects of hyperplane sections of polytopes, focusing on how much the combinatorics of the sections determines the combinatorics of the original polytope. We…
Critical moments of slices and slabs of the cube (and other polyhedral norms)
Marie-Charlotte Brandenburg, Jesús A. De Loera, Yu Luo +1
In this article, we present a unified algebraic-combinatorial framework for computing explicit, piecewise rational, and combinatorially indexed parametric formulas for volumes and…
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…
Veronese polytopes: Extending the framework of cyclic polytopes
Marie-Charlotte Brandenburg, Roland Púček
This article introduces the theory of Veronese polytopes, a broad generalisation of cyclic polytopes. These arise as convex hulls of points on curves with one or more connected com…
Decomposition Polyhedra of Piecewise Linear Functions
Marie-Charlotte Brandenburg, Moritz Grillo, Christoph Hertrich
In this paper we contribute to the frequently studied question of how to decompose a continuous piecewise linear (CPWL) function into a difference of two convex CPWL functions. Eve…
The Real Tropical Geometry of Neural Networks
Marie-Charlotte Brandenburg, Georg Loho, Guido Montúfar
We consider a binary classifier defined as the sign of a tropical rational function, that is, as the difference of two convex piecewise linear functions. The parameter space of ReL…
Quotients of M-convex sets and M-convex functions
Marie-Charlotte Brandenburg, Georg Loho, Ben Smith
We unify the study of quotients of matroids, polymatroids, valuated matroids and strong maps of submodular functions in the framework of Murota's discrete convex analysis. As a mai…
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…
Combinatorics of Correlated Equilibria
Marie-Charlotte Brandenburg, Benjamin Hollering, Irem Portakal
We study the correlated equilibrium polytope of a game from a combinatorial point of view. We introduce the region of full-dimensionality for this class of polytopes and…
Tropical Positivity and Determinantal Varieties
Marie-Charlotte Brandenburg, Georg Loho, Rainer Sinn
We initiate the study of positive-tropical generators as positive analogues of the concept of tropical bases. Applying this to the tropicalization of determinantal varieties, we de…
Competitive equilibrium always exists for combinatorial auctions with graphical pricing schemes
Marie-Charlotte Brandenburg, Christian Haase, Ngoc Mai Tran
We show that a competitive equilibrium always exists in combinatorial auctions with anonymous graphical valuations and pricing, using discrete geometry. This is an intuitive and ea…
Multivariate volume, Ehrhart, and -polynomials of polytropes
Marie-Charlotte Brandenburg, Sophia Elia, Leon Zhang
The univariate Ehrhart and -polynomials of lattice polytopes have been widely studied. We describe methods from toric geometry for computing multivariate versions of volume, E…