Simplicial Arrangements with up to 27 Lines

M. Cuntz

doi:10.1007/s00454-012-9423-7

Simplicial Arrangements with up to 27 Lines

M. Cuntz^*

^*Corresponding author for this work

University of Kaiserslautern

Research output: Contribution to journal › Article › Research › peer review

Abstract

We compute all isomorphism classes of simplicial arrangements in the real projective plane with up to 27 lines. It turns out that Grünbaum's catalogue is complete up to 27 lines except for four new arrangements with 22, 23, 24, 25 lines, respectively. As a byproduct we classify simplicial arrangements of pseudolines with up to 27 lines. In particular, we disprove Grünbaum's conjecture about unstretchable arrangements with at most 16 lines, and prove the conjecture that any simplicial arrangement with at most 14 pseudolines is stretchable.

Original language	English
Pages (from-to)	682-701
Number of pages	20
Journal	Discrete and Computational Geometry
Volume	48
Issue number	3
DOIs	https://doi.org/10.1007/s00454-012-9423-7
Publication status	Published - 1 Oct 2012
Externally published	Yes

Keywords

Arrangement of hyperplanes
Pseudoline
Simplicial
Wiring

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-012-9423-7

Cite this

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AB - We compute all isomorphism classes of simplicial arrangements in the real projective plane with up to 27 lines. It turns out that Grünbaum's catalogue is complete up to 27 lines except for four new arrangements with 22, 23, 24, 25 lines, respectively. As a byproduct we classify simplicial arrangements of pseudolines with up to 27 lines. In particular, we disprove Grünbaum's conjecture about unstretchable arrangements with at most 16 lines, and prove the conjecture that any simplicial arrangement with at most 14 pseudolines is stretchable.

KW - Arrangement of hyperplanes

KW - Pseudoline

KW - Simplicial

KW - Wiring

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ER -

Simplicial Arrangements with up to 27 Lines

Abstract

Keywords

ASJC Scopus subject areas

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