Shellable tilings on relative simplicial complexes and their <i>h</i>-vectors

New methods for constructing shellable simplicial complexes

A clutter $mathcal{C}$ with vertex set $[n]$ is an antichain of subsets of $[n]$, called circuits, covering all vertices. The clutter is $d$-uniform if all of its circuits have the same cardinality $d$. If $mathbb{K}$ is a field, then there is a one-to-one correspondence between clutters on $V$ and square-free monomial ideals in $mathbb{K}[x_1,ldots,x_n]$ as follows: To each clutter $mathcal{C}...

On Isomorphism of Simplicial Complexes and Their Related Algebras

Balanced Vertex Decomposable Simplicial Complexes and their h-vectors

Given any finite simplicial complex ∆, we show how to construct from a colouring χ of ∆ a new simplicial complex ∆χ that is balanced and vertex decomposable. In addition, the h-vector of ∆χ is precisely the f -vector of ∆. Our construction generalizes the “whiskering” construction of Villarreal, and Cook and Nagel. We also reverse this construction to prove a special case of a conjecture of Coo...

on isomorphism of simplicial complexes and their related algebras

Simplicial Shellable Spheres via Combinatorial Blowups

The construction of the Bier sphere Bier(K) for a simplicial complex K is due to Bier (1992). Björner, Paffenholz, Sjöstrand and Ziegler (2005) generalize this construction to obtain a Bier poset Bier(P, I) from any bounded poset P and any proper ideal I ⊆ P . They show shellability of Bier(P, I) for the case P = Bn, the boolean lattice, and thereby obtain ‘many shellable spheres’ in the sense ...