A Proof of the Strict Monotone 5-step Conjecture

J. Mackenzie Gallagher; Walter D. Morris,

A Proof of the Strict Monotone 5-step Conjecture

Combinatorics 2018-07-02 v2

Authors: J. Mackenzie Gallagher , Walter D. Morris,

Abstract

A computer search through the oriented matroid programs with dimension 5 and 10 facets shows that the maximum strictly monotone diameter is 5. Thus $\Delta_{sm}(5,10)=5$ . This enumeration is analogous to that of Bremner and Schewe for the non-monotone diameter of 6-polytopes with 12 facets. Similar enumerations show that $\Delta_{sm}(4,9)=5$ and $\Delta_m(4,9)=\Delta_m(5,10)=6.$ We shorten the known non-computer proof of the strict monotone 4-step conjecture.

Keywords

polytopes set theory and dimension theory

Cite

@article{arxiv.1806.03403,
  title  = {A Proof of the Strict Monotone 5-step Conjecture},
  author = {J. Mackenzie Gallagher and Walter D. Morris,},
  journal= {arXiv preprint arXiv:1806.03403},
  year   = {2018}
}

Comments

In Sections 2 and 3, "n-d" and "d" had been switched

A Proof of the Strict Monotone 5-step Conjecture

Abstract

Keywords

Cite

Comments

Related papers