Triangulations of polygons and stacked simplicial complexes: separating their Stanley–Reisner ideals

Tchebyshev triangulations of stable simplicial complexes

We generalize the notion of the Tchebyshev transform of a graded poset to a triangulation of an arbitrary simplicial complex in such a way that, at the level of the associated F -polynomials ∑ j fj−1((x − 1)/2), the triangulation induces taking the Tchebyshev transform of the first kind. We also present a related multiset of simplicial complexes whose association induces taking the Tchebyshev t...

On Isomorphism of Simplicial Complexes and Their Related Algebras

on isomorphism of simplicial complexes and their related algebras

Triangulations of Simplicial Polytopes

Various facts about triangulations of simplicial polytopes, particularly those pertaining to the equality case in the generalized lower bound conjecture, are collected together here. They include an apparently weaker restriction on the kind of triangulation which needs to be found, and an inductive argument which reduces the number of cases to be established.

Hamiltonian Triangulations and Circumscribing Polygons

Let Σ = { S1 , . . . , Sn } be a finite set of disjoint line segments in the plane. We conjecture that its visibility graph, Vis(Σ), is hamiltonian. In fact, we make the stronger conjecture that Vis(Σ) has a hamiltonian cycle whose embedded version is a simple polygon (i.e., its boundary edges are non-crossing visibility segments). We call such a simple polygon a spanning polygon of Σ. Existenc...