Work

Reconstruction of slices of cubes

Year: 2026

Type: preprint

Abstract: 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 cannot extend to slices of arbitrary simple polytopes by constructing a simple polytope that has two combinatorially distinct slices with isomorphic graphs.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.09939

Authors: Brandenburg, Marie-Charlotte, Curtis, Juliana, Giardino, Chiara, Meroni, Chiara, Padrol, Arnau

Institutions: Ruhr University Bochum, University of Washington, ETH Institute for Theoretical Studies, Centre de Recerca Matemàtica, Universitat de Barcelona

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Universitat de Barcelona, ETH Zürich Foundation, Agencia Estatal de Investigación

Awards: G1791683384, G2766336479, G4532494212, G5893294622, G84477964

OpenAlex ID: W7220926416

Cites: 16

Cited by:

Related to: 10