Work

Deformation cones of 2-cubical combinatorial zonotopes

Year: 2026

Type: preprint

Abstract: We prove that the dimension of the deformation cone of any polytope combinatorially equivalent to a 2-cubical zonotope is bounded above by the number of generators of the zonotope. This bound is tight, and we show that it cannot be improved to an identity. We further extend our results to any 2-cubical polytope whose normal fan is combinatorially isomorphic to a pseudohyperplane arrangement, but we show that it cannot be extended to arbitrary 2-cubical polytopes.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.13441

Authors: Curtis, Juliana, O'Brien, Grace, Padrol, Arnau, Poullot, Germain

Institutions: University of Washington, 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: National Science Foundation, Deutsche Forschungsgemeinschaft, Universitat de Barcelona, Agencia Estatal de Investigación

Awards: G1791683384, G2766336479, G4532494212, G84477964, Graduate Research Fellowship Program (GRFP)

OpenAlex ID: W7221508687

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