منابع مشابه
Simplicial Moves on Balanced Complexes
We introduce a notion of cross-flips: local moves that transform a balanced (i.e., properly (d + 1)-colored) triangulation of a combinatorial d-manifold into another balanced triangulation. These moves form a natural analog of bistellar flips (also known as Pachner moves). Specifically, we establish the following theorem: any two balanced triangulations of a closed combinatorial d-manifold can ...
متن کاملSimplicial moves on complexes and manifolds
Here are versions of the proofs of two classic theorems of combinatorial topology. The first is the result that piecewise linearly homeomorphic simplicial complexes are related by stellar moves. This is used in the proof, modelled on that of Pachner, of the second theorem. This states that moves from only a finite collection are needed to relate two triangulations of a piecewise linear manifold...
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We establish an upper bound on the cardinality of a minimal generating set for the fundamental group of a large family of connected, balanced simplicial complexes and, more generally, simplicial posets.
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Given any finite simplicial complex ∆, we show how to construct from a colouring χ of ∆ a new simplicial complex ∆χ that is balanced and vertex decomposable. In addition, the h-vector of ∆χ is precisely the f -vector of ∆. Our construction generalizes the “whiskering” construction of Villarreal, and Cook and Nagel. We also reverse this construction to prove a special case of a conjecture of Coo...
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Given a graph G, the number of nowhere-zero Zq-flows φG(q) is known to be a polynomial in q. We extend the definition of nowhere-zero Zq-flows to simplicial complexes ∆ of dimension greater than one, and prove the polynomiality of the corresponding function φ∆(q) for certain q and certain subclasses of simplicial complexes. Résumé. Et́ant donné une graphe G, on est connu que le nombre de Zq-flot...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2017
ISSN: 0001-8708
DOI: 10.1016/j.aim.2017.08.036