In this note we introduce the concept of the trade space of a latin square. Computations using Sage and the GAP package Simplicial Homology are presented.

For any orbifold M, we explicitly construct a simplicial complex S(M) from a given triangulation of the ‘coarse’ underlying space together with the local isotropy groups of M. We prove that, for any local system on M, this complex S(M) has the same cohomology as M. The use of S(M) in explicit calculations is illustrated in the example of the ‘teardrop’ orbifold.

For each finite real reflection group W , we identify a copy of the type-W simplicial generalised associahedron inside the corresponding simplicial permutahedron. This defines a bijection between the facets of the generalised associahedron and the elements of the type W non-crossing partition lattice which is more tractable than previous such bijections. We show that the simplicial fan determin...

Figure 1: Two greatly different curves have a small Hausdroff distance Fréchet distance is a good similarity measurement for curves in Euclidean space. It can be simply described by a daily example. Suppose a dog and its owner are walking along two different paths (curves), connected by a leash. Both of them are moving continuously and forwards only, at any speed or even stop. Then length of th...

Let K be a nonarchimedean local field, for example the p-adic numbers Qp (char(K) = 0) or the field of Laurent series over a finite field Fp((t)) (char(p) > 0) . Let G = PGLn(K), or more generally the K-points of any absolutely simple, connected, algebraic K-group of adjoint form. There is a natural way to associate to each cocompact lattice Γ in G a finite simplicial complex BΓ, as follows. Br...

simplicial complex. An abstract simplicial complex is a set {1, ..., N} with a set K of subsets such that if Y ∈ K and X ⊂ Y then X ∈ K. In other words, every subset of a subset in K is also included in K. Every simplicial complex is an abstract simplicial complex, where the elements of the set {1, ..., N} correspond to labelled vertices, and the set of subsets K corresponds to simplices (toget...