A Proof of the Strict Monotone 5-Step Conjecture

A Proof of the Strict Monotone 5-Step Conjecture

A computer search through the oriented matroid programs with dimension 5 and 10 facets shows that the maximum strictly monotone diameter is 5. Thus Δ sm ( 5 , 10 ) = 5 . This enumeration is analogous to that of Bremner and Schewe for the non-monotone diameter of 6-polytopes with 12 facets. A similar...

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Veröffentlicht in:Discrete & computational geometry 2021-03, Vol.65 (2), p.476-488
Hauptverfasser: Gallagher, John Mackenzie, Morris, Walter D.
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Computational Mathematics and Numerical Analysis
Diameters
Enumeration
Mathematics
Mathematics and Statistics
Polytopes
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Zusammenfassung:A computer search through the oriented matroid programs with dimension 5 and 10 facets shows that the maximum strictly monotone diameter is 5. Thus Δ sm ( 5 , 10 ) = 5 . This enumeration is analogous to that of Bremner and Schewe for the non-monotone diameter of 6-polytopes with 12 facets. A similar search shows that Δ m ( 5 , 10 ) = 6 . We provide a short non-computer proof of Δ sm ( 4 , 8 ) = 4 .
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-019-00161-3