Two counterexamples for power ideals of arrangements

2012/11/06 by Ardila, Federico, Postnikov, Alex
#05A15 #05B35 #13P99 #41A15 #52C35 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1211.1368

Abstract

We disprove Holtz and Ron's conjecture that the power ideal C_A,-2 of a hyperplane arrangement A (also called the "internal zonotopal space") is generated by A-monomials. We also show that, in contrast with the case k ≥ -2, the Hilbert series of C_A,k is not determined by the matroid of A for k ≤ -6.

Related

• Combinatorics and geometry of power ideals
• Projection volumes of hyperplane arrangements
• On power ideals of transversal matroids and their "parking functions"
• Classification of external Zonotopal algebras
• Hilbert series of subspace arrangements