Occupants in simplicial complexes
نویسندگان
چکیده
منابع مشابه
New 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 کاملCentralities in Simplicial Complexes
Complex networks can be used to represent complex systems which originate in the real world. Here we study a transformation of these complex networks into simplicial complexes, where cliques represent the simplices of the complex. We extend the concept of node centrality to that of simplicial centrality and study several mathematical properties of degree, closeness, betweenness, eigenvector, Ka...
متن کاملIsoperimetric inequalities in simplicial complexes
In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a complex, and the spectrum of the high dimensional Laplacian defined by Eckmann. In...
متن کاملSaturated simplicial complexes
Among shellable complexes a certain class has maximal modular homology, and these are the so-called saturated complexes. We extend the notion of saturation to arbitrary pure complexes and give a survey of their properties. It is shown that saturated complexes can be characterized via the p -rank of incidence matrices and via the structure of links. We show that rank-selected subcomplexes of sat...
متن کاملCompletions and Simplicial Complexes
We first introduce the notion of a completion. Completions are inductive properties which may be expressed in a declarative way and which may be combined. We show that completions may be used for describing structures or transformations which appear in combinatorial topology. We present two completions, 〈CUP〉 and 〈CAP〉, in order to define, in an axiomatic way, a remarkable collection of acyclic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2019
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2019.19.1265