Characteristic Lattice Complexes

Factoring the characteristic polynomial of a lattice

Article history: Received 31 October 2014 Available online xxxx

Simplicial Complexes with Lattice Structures

If L is a finite lattice, we show that there is a natural topological lattice structure on the geometric realization of its order complex ∆(L) (definition recalled below). Lattice-theoretically, the resulting object is a subdirect product of copies of L. We note properties of this construction and of some variants, and pose several questions. For M3 the 5-element nondistributive modular lattice...

Lattice paths and generalized cluster complexes

In this talk we will introduce/survey the cluster complexes of Fomin and Zelevinsky, generalized cluster complexes of Fomin and Reading, and their associated M, F, H triangles by Chapoton, Armstrong and Krattenthaler respectively. After that we propose a variant of the generalized Schröder paths and generalized Delannoy paths by giving a restriction on the positions of certain steps. This pure ...

Chromatic Numbers, Morphism Complexes, and Stiefel-whitney Characteristic Classes

Complexity and Algorithms for Euler Characteristic of Simplicial Complexes

We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler characteristic. The two new algorithms are derived using combinatorial commutative algebra and we also give a second description of them that requires no algebra. We...