Topology of Augmented Bergman Complexes
نویسندگان
چکیده
The augmented Bergman complex of a matroid is simplicial introduced recently in work Braden, Huh, Matherne, Proudfoot and Wang. It may be viewed as hybrid two well-studied pure shellable complexes associated to matroids: the independent set complex.
 shown here that also shellable, via different families shelling orders. Furthermore, comparing description its homotopy type induced from shellings re-interprets known convolution formula counting bases matroid. representation automorphism group on homology turns out have surprisingly simple description. This last fact generalized closures beyond those coming
منابع مشابه
Bergman Complexes
Tropical varieties play an important role in algebraic geometry. The Bergman complex B(M) and the positive Bergman complex B+(M) of an oriented matroid M generalize to matroids the notions of the tropical variety and positive tropical variety associated to a linear ideal. Our main result is that if A is a Coxeter arrangement of type Φ with corresponding oriented matroid MΦ, then B (MΦ) is dual ...
متن کاملBergman Complexes, Coxeter Arrangements, and Graph Associahedra
Tropical varieties play an important role in algebraic geometry. The Bergman complex B(M) and the positive Bergman complex B+(M) of an oriented matroid M generalize to matroids the notions of the tropical variety and positive tropical variety associated to a linear ideal. Our main result is that if A is a Coxeter arrangement of type Φ with corresponding oriented matroid MΦ, then B (MΦ) is dual ...
متن کاملTopology of Cell Complexes
(3) X = ⋃ n X n with the weak topology: A set A ⊂ X is open (or closed) iff A∩X is open (or closed) in X for each n . Note that condition (3) is superfluous when X is finite-dimensional, so that X = X for some n . For if A is open in X = X , the definition of the quotient topology on X implies that A∩X is open in X , and then by the same reasoning A∩X is open in X , and similarly for all the sk...
متن کاملComputational Topology Simplicial Complexes
In the first lecture, we looked at concepts from point set topology, the branch of topology that studies continuity from an analytical point of view. This view does not have a computational nature: we cannot represent infinite point sets or their associated infinite open sets on a computer. Starting with this lecture, we will look at concepts from another major branch of topology: combinatorial...
متن کاملTopology of random clique complexes
In a seminal paper, Erdős and Rényi identified a sharp threshold for connectivity of the random graph G(n, p). In particular, they showed that if p log n/n then G(n, p) is almost always connected, and if p log n/n then G(n, p) is almost always disconnected, as n→∞. The clique complex X (H) of a graph H is the simplicial complex with all complete subgraphs of H as its faces. In contrast to the z...
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: Electronic Journal of Combinatorics
سال: 2022
ISSN: ['1077-8926', '1097-1440']
DOI: https://doi.org/10.37236/10739