1 citations · 3 across the 11 of their papers we have counts for
17 papers
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…
From Ham-Sandwich to Centerpoints: Semialgebraic Algorithms for Cutting Polytopal Measures
Marie-Charlotte Brandenburg, Jesús A. De Loera, Chiara Meroni
We design exact algorithms for the ham-sandwich and centerpoint theorems for polytopal measures. Our key observation is that the cap-volume function of such a measure, i.e., the vo…
Benchmarks in Leipzig
Andrei Balakin, Miklós Bóna, Marie-Charlotte Brandenburg +45
Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers. Most of the work was done during the 3…
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…
How to Learn a Star: Binary Classification with Starshaped Polyhedral Sets
Marie-Charlotte Brandenburg, Katharina Jochemko
We consider binary classification restricted to a class of continuous piecewise linear functions whose decision boundaries are (possibly nonconvex) starshaped polyhedral sets, supp…