A Proof of the Strict Monotone 5-step Conjecture

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.

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