منابع مشابه
Bier Spheres and Posets
In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n− 2)-spheres on 2n vertices as deleted joins of a simplicial complex on n vertices with its combinatorial Alexander dual. Here we interpret his construction as giving the poset of all the intervals in a boolean algebra that “cut across an ideal.” Thus we arrive at a substantial generalization of Bi...
متن کاملOn Barycentric Subdivision
Consider the barycentric subdivision which cuts a given triangle along its medians to produce six new triangles. Uniformly choosing one of them and iterating this procedure gives rise to a Markov chain. We show that almost surely, the triangles forming this chain become flatter and flatter in the sense that their isoperimetric values goes to infinity with time. Nevertheless, if the triangles ar...
متن کاملUniversality for Barycentric subdivision
The spectrum of the Laplacian of successive Barycentric subdivisions of a graph converges exponentially fast to a limit which only depends on the clique number of the initial graph and not on the graph itself. Announced in [40]), the proof uses now an explicit linear operator mapping the clique vector of a graph to the clique vector of the Barycentric refinement. The eigenvectors of its transpo...
متن کاملBarycentric Subspaces Analysis on Spheres
This paper addresses the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. Current methods like Principal Geodesic Analysis (PGA) and Geodesic PCA (GPCA) minimize the distance to a ”Geodesic subspace”. This allows to build sequences of nested subspaces which are consistent with a forward component analysis approach. However, these methods cannot easily be adapted to ...
متن کاملBarycentric Subdivision and Isomorphisms of Groupoids
Given groupoids G and H as well as an isomorphism Ψ : Sd G∼= Sd Hbetween subdivisions, we construct an isomorphism P : G∼= H . If Ψ equals SdF forsome functor F , then the constructed isomorphism P is equal to F . It follows thatthe restriction of Sd to the category of groupoids is conservative. These results donot hold for arbitrary categories.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2004
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2003.12.002