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 \(\Delta_{sm}(5,10)=5\). 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.