enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Abstract simplicial complex - Wikipedia

    en.wikipedia.org/wiki/Abstract_simplicial_complex

    One-dimensional abstract simplicial complexes are mathematically equivalent to simple undirected graphs: the vertex set of the complex can be viewed as the vertex set of a graph, and the two-element facets of the complex correspond to undirected edges of a graph. In this view, one-element facets of a complex correspond to isolated vertices that ...

  3. Poset topology - Wikipedia

    en.wikipedia.org/wiki/Poset_topology

    The order complex associated to a poset (S, ≤) has the set S as vertices, and the finite chains of (S, ≤) as faces. The poset topology associated to a poset ( S , ≤) is then the Alexandrov topology on the order complex associated to ( S , ≤).

  4. Alexander duality - Wikipedia

    en.wikipedia.org/wiki/Alexander_duality

    That is, the correct answer in honest Betti numbers is 2, 0, 0. Once more, it is the reduced Betti numbers that work out. With those, we begin with 0, 1, 0. to finish with 1, 0, 0. From these two examples, therefore, Alexander's formulation can be inferred: reduced Betti numbers ~ are related in complements by

  5. h-vector - Wikipedia

    en.wikipedia.org/wiki/H-vector

    Let Δ be an abstract simplicial complex of dimension d − 1 with f i i-dimensional faces and f −1 = 1. These numbers are arranged into the f-vector of Δ, = (,, …,).An important special case occurs when Δ is the boundary of a d-dimensional convex polytope.

  6. Kruskal–Katona theorem - Wikipedia

    en.wikipedia.org/wiki/Kruskal–Katona_theorem

    In algebraic combinatorics, the Kruskal–Katona theorem gives a complete characterization of the f-vectors of abstract simplicial complexes.It includes as a special case the ErdÅ‘s–Ko–Rado theorem and can be restated in terms of uniform hypergraphs.

  7. Simplicial complex recognition problem - Wikipedia

    en.wikipedia.org/wiki/Simplicial_complex...

    An abstract simplicial complex (ASC) is family of sets that is closed under taking subsets (the subset of a set in the family is also a set in the family). Every abstract simplicial complex has a unique geometric realization in a Euclidean space as a geometric simplicial complex (GSC), where each set with k elements in the ASC is mapped to a (k-1)-dimensional simplex in the GSC.

  8. AOL Mail

    mail.aol.com

    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

  9. Family of sets - Wikipedia

    en.wikipedia.org/wiki/Family_of_sets

    An abstract simplicial complex is a combinatorial abstraction of the notion of a simplicial complex, a shape formed by unions of line segments, triangles, tetrahedra, and higher-dimensional simplices, joined face to face. In an abstract simplicial complex, each simplex is represented simply as the set of its vertices.