Zurück zu den Preprints des Jahres 2007


2007-08

4-Polymatroids and the corresponding rank functions

by Bacic, L., Baradyntsau, A., Sauchanka, A., Girlich, E..


Series: 2007-08, Preprints

MSC:
90B10 Network models, 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