The stable set of associated prime ideals of a polymatroidal ideal

2011/09/27 by Herzog, Jürgen, Rauf, Asia, Vladoiu, Marius · 4 citations
#05E40 #13A30 #13C13 #13F99 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.5834

Abstract

The associated prime ideals of powers of polymatroidal ideals are studied, including the stable set of associated prime ideals of this class of ideals. It is shown that polymatroidal ideals have the persistence property and for transversal polymatroids and polymatroidal ideals of Veronese type the index of stability and the stable set of associated ideals is determined explicitly.

Cited by

• Homological shifts of powers a complementary edge ideal
• Criteria for the presence of the maximal ideal in the set of associated primes
• Polymatroidal ideals and their asymptotic syzygies
• Depth and regularity of powers of edge ideals of edge-weighted trees

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