A Proof of the Strict Monotone 5-step Conjecture


Abstract in English

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.

Download