Flows on Simplicial Complexes
نویسندگان
چکیده
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-flots non-nuls G (q) est un polynˆome dans q. Nous étendons la définition de Zq-flots non-nuls pour incluir des complexes simpliciaux de dimension plus grande qu’un, et on montre que le nombre est aussi un polynˆome de la fonction correspondante pour certain valeurs de q et de certaines sous-classes de complexes simpliciaux.
منابع مشابه
Cohen-Macaulay-ness in codimension for simplicial complexes and expansion functor
In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $tgeq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we provethat it can be obtained from a Buchsbaum complex.
متن کاملVertex Decomposable Simplicial Complexes Associated to Path Graphs
Introduction Vertex decomposability of a simplicial complex is a combinatorial topological concept which is related to the algebraic properties of the Stanley-Reisner ring of the simplicial complex. This notion was first defined by Provan and Billera in 1980 for k-decomposable pure complexes which is known as vertex decomposable when . Later Bjorner and Wachs extended this concept to non-pure ...
متن کاملNew methods for constructing shellable simplicial complexes
A clutter $mathcal{C}$ with vertex set $[n]$ is an antichain of subsets of $[n]$, called circuits, covering all vertices. The clutter is $d$-uniform if all of its circuits have the same cardinality $d$. If $mathbb{K}$ is a field, then there is a one-to-one correspondence between clutters on $V$ and square-free monomial ideals in $mathbb{K}[x_1,ldots,x_n]$ as follows: To each clutter $mathcal{C}...
متن کاملSolving 1-Laplacians in Nearly Linear Time: Collapsing and Expanding a Topological Ball
Abstract We present an e cient algorithm for solving a linear system arising from the 1-Laplacian of a collapsible simplicial complex with a known collapsing sequence. When combined with a result of Chillingworth, our algorithm is applicable to convex simplicial complexes embedded in R. The running time of our algorithm is nearly-linear in the size of the complex and is logarithmic on its numer...
متن کامل