Tchebyshev triangulations of stable simplicial complexes

Pseudo-tetrahedral complexes

A pseudo-triangulation is a cell complex in the plane whose cells are pseudo-triangles, i.e., simple polygons with exactly three convex vertices (so-called corners). Being an interesting and flexible generalization of triangulations, pseudo-triangulations have found their place in computational geometry; see e.g. [8, 11, 7, 1] and references therein. Unlike triangulations, pseudo-triangulations...

Subword complexes, cluster complexes, and generalized multi-associahedra

In this paper, we use subword complexes to provide a uniform approach to finite-type cluster complexes and multi-associahedra. We introduce, for any finite Coxeter group and any nonnegative integer k, a spherical subword complex called multi-cluster complex. For k = 1, we show that this subword complex is isomorphic to the cluster complex of the given type. We show that multi-cluster complexes ...

Buchsbaum* Complexes

A class of finite simplicial complexes, which we call Buchsbaum* over a field, is introduced. Buchsbaum* complexes generalize triangulations of orientable homology manifolds as well as doubly Cohen-Macaulay complexes. By definition, the Buchsbaum* property depends only on the geometric realization and the field. Characterizations in terms of simplicial homology are given. It is proved that Buch...

Tchebyshev Posets

We construct for each n an Eulerian partially ordered set Tn of rank n + 1 whose ce-index provides a non-commutative generalization of the n-th Tchebyshev polynomial. We show that the order complex of each Tn is shellable, homeomorphic to a sphere, and that its face numbers minimize the expression max|x|≤1 ∣∣∣∑nj=0(fj−1/fn−1) · 2−j · (x− 1)j∣∣∣ among the f -vectors of all (n − 1)-dimensional si...

On Isomorphism of Simplicial Complexes and Their Related Algebras