Criterions for Shellable Multicomplexes

Abstract

After [J.Herzog, D.Popescu, Finite filtrations of modules and shellable multicomplexes, Preprint IMAR no 4/2005, Bucharest, 2005], the shellability of multicomplexes $\Gamma$ is given in terms of some special faces of $\Gamma$ called facets. Here we give a criterion for the shellability in terms of maximal facets. Multigraded pretty clean filtration is the algebraic counterpart of a shellable multicomplex. We give also a criterion for the existence of a multigraded pretty clean filtration.

10 pages

Cited by in corpus (8)

• Stanley Conjecture in small embedding dimension
• An inequality between depth and Stanley depth
• Sequentially Cohen-Macaulay monomial ideals of embedding dimension four
• Stanley Depth of Multigraded Modules
• Monomial ideals with linear quotients and componentwise (support-)linearity
• An Efficient Algebraic Criterion for Shellability
• Linear Residuals and Gallai-Simplicial Complexes
• Stanley Decompositions and Polarization