Nearly neighbourly families of standard boxes

Jacek Bojarski; Andrzej P. Kisielewicz; Krzysztof Przesławski

Nearly neighbourly families of standard boxes

Combinatorics 2016-07-28 v1

Authors: Jacek Bojarski , Andrzej P. Kisielewicz , Krzysztof Przesławski

Abstract

It is demonstrated that each nearly neighbourly family of standard boxes in $\mathbb{R}^3$ has at most 12 elements. A combinatorial classification of all such families that have exactly 12 elements is given. All families satisfying an extra property called incompressibility are described. Compressible families are discussed briefly.

Keywords

nearly neighbourly families standard boxes combinatorial classification incompressibility convex geometry

Cite

@article{arxiv.1607.08195,
  title  = {Nearly neighbourly families of standard boxes},
  author = {Jacek Bojarski and Andrzej P. Kisielewicz and Krzysztof Przesławski},
  journal= {arXiv preprint arXiv:1607.08195},
  year   = {2016}
}

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37 pages, 10 figures, 22 tables

Nearly neighbourly families of standard boxes

Abstract

Keywords

Cite

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