07-08
4-Polymatroids and the corresponding rank functions
by Bacic, L.; Baradyntsau, A.; Sauchanka, A.; Girlich, E.
Preprint series: 07-08, Preprints
- MSC:
- 90B10 Flows in networks, deterministic
Abstract: 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.
Keywords: polymatroid, structure of the facet set, polyhedra type
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