Prime filtrations of monomial ideals and polarizations

By Ali Soleyman Jahan. 2006

67 citations recorded by the source corpus.

Abstract We show that an arbitrary monomial ideal I is pretty clean if and only if its polarization I p is clean. This yields a new characterization of pretty clean monomial ideals in terms of the arithmetic degree, and it also implies that a multicomplex is shellable if and only the simplicial complex corresponding to its polarization is (non-pure) shellable. We also discuss Stanley decompositions in relation to prime filtrations.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/77a3c9f37dfb2d3d1135032925690c65197d8bf1

Citations in the corpus

• How to compute the Stanley depth of a monomial ideal (2007, unknown): “12 13 14 23 24 34 123 124 134 234 1234 Let A = [1,12] ∪ [2,23] ∪ [3,34] ∪ [4,14].”