by Bacic, L., Baradyntsau, A., Sauchanka, A., Girlich, E..
Series: 2007-08, Preprints
Polymatroids are special polyhedra, that can be generated by submodular, monotone and normalized
functions r(I), the so-called rank functions. In this article we summarize general properties
and theorems and explain them by using 4 dimensional polymatroids. The term of combinatorial
equivalence of polyhedra is used to classify polymatroids. In the 4-dimensional space
the number of polymatroids is finite and we try to estimate its upper and lower bounds. Besides,
we study important structures of the family of facets.
polymatroid, structure of the facet set, polyhedra type