English

Geodesics in CAT(0) Cubical Complexes

Combinatorics 2015-03-17 v1 Computational Geometry Discrete Mathematics Metric Geometry

Abstract

We describe an algorithm to compute the geodesics in an arbitrary CAT(0) cubical complex. A key tool is a correspondence between cubical complexes of global non-positive curvature and posets with inconsistent pairs. This correspondence also gives an explicit realization of such a complex as the state complex of a reconfigurable system, and a way to embed any interval in the integer lattice cubing of its dimension.

Keywords

Cite

@article{arxiv.1101.2428,
  title  = {Geodesics in CAT(0) Cubical Complexes},
  author = {Federico Ardila and Megan Owen and Seth Sullivant},
  journal= {arXiv preprint arXiv:1101.2428},
  year   = {2015}
}

Comments

27 pages, 7 figures

R2 v1 2026-06-21T17:11:11.168Z