In Chapter 12 we consider discrete polymatroids and polymatroidal ideals. After giving a short introduction to the combinatorics and geometry of discrete polymatroids, the algebraic properties of its base ring are studied. We close Chapter 12 by presenting polymatroidal and weakly polymatroidal ideals, which provide large classes of ideals with linear quotients.
KeywordsRank Function Exchange Property Monomial Ideal Integer Vector Submodular Function
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