2 papers
math.CO2018
A Proof of the Strict Monotone 5-step Conjecture
J. Mackenzie Gallagher, Walter D. Morris
A computer search through the oriented matroid programs with dimension 5 and 10 facets shows that the maximum strictly monotone diameter is 5. Thus . This enumerati…
math.CO2016
Tail diameter upper bounds for polytopes and polyhedra
J. Mackenzie Gallagher, Edward D. Kim
In 1992, Kalai and Kleitman proved a quasipolynomial upper bound on the diameters of convex polyhedra. Todd and Sukegawa-Kitahara proved tail-quasipolynomial bounds on the diameter…