31 research outputs found
Unshellable Triangulations of Spheres
A direct proof is given of the existence of non-shellable triangulations of spheres which, in higher dimensions, yields new examples of such triangulations
Small examples of non-constructible simplicial balls and spheres
We construct non-constructible simplicial -spheres with vertices
and non-constructible, non-realizable simplicial -balls with vertices
for .Comment: 9 pages, 3 figure
On the non-existence of an R-labeling
We present a family of Eulerian posets which does not have any R-labeling.
The result uses a structure theorem for R-labelings of the butterfly poset.Comment: 6 pages, 1 figure. To appear in the journal Orde
Collapses, products and LC manifolds
Durhuus and Jonsson (1995) introduced the class of "locally constructible"
(LC) triangulated manifolds and showed that all the LC 2- and 3-manifolds are
spheres. We show here that for each d>3 some LC d-manifolds are not spheres. We
prove this result by studying how to collapse products of manifolds with
exactly one facet removed.Comment: 6 pages; added references; minor changes. Accepted for J. Comb.
Theory, Series
Glicci simplicial complexes
One of the main open questions in liaison theory is whether every homogeneous
Cohen-Macaulay ideal in a polynomial ring is glicci, i.e. if it is in the
G-liaison class of a complete intersection. We give an affirmative answer to
this question for Stanley-Reisner ideals defined by simplicial complexes that
are weakly vertex-decomposable. This class of complexes includes matroid,
shifted and Gorenstein complexes respectively. Moreover, we construct a
simplicial complex which shows that the property of being glicci depends on the
characteristic of the base field. As an application of our methods we establish
new evidence for two conjectures of Stanley on partitionable complexes and on
Stanley decompositions