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Geometric and Combinatorial Properties of the Alternating Sign Matrix Polytope
Elizabeth A. Dinkelman, Walter D. Morris
The polytope , the convex hull of the alternating sign matrices, was introduced by Striker and by Behrend and Knight. A face of corresponds to an element…
On the Holt-Klee Property for Oriented Matroid Programming
Walter D. Morris
The Holt-Klee theorem says that the graph of a -polytope, with edges oriented by a linear function on that is not constant on any edge, admits independent monotone paths…
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…
On Minkowski Sums of Simplices
Geir Agnarsson, Walter Morris
We investigate the structure of the Minkowski sum of standard simplices in . In particular, we investigate the one-dimensional structure, the vertices, their degrees an…