All Questions
Tagged with euler-characteristics co.combinatorics
4 questions
5
votes
0
answers
244
views
Does the (Poincare) dual complex represent the same topology?
To start with, consider some abstract $3$-dimensional simplicial complex $\Delta$ representing a manifold without boundary, for simplicity. Then, there is this well-known construction of the "(...
- 1,171
8
votes
2
answers
294
views
Euler characteristic of the simplicial complex of sets of elements in a semilattice with non-zero meet
In a combinatorial computation, I came across the following quantity:
Consider a finite meet semilattice $L$, that is, a finite poset which is closed under $\min$. Denote the least element of $L$ by $...
- 305
6
votes
0
answers
289
views
Is Euler-characteristic of a simplicial complex on $n$ vertices and $f$ facets at most $n^{O(\log f)}$?
(Definition: Facet = Maximal Face)
This question is a continuation of the previous one that I had asked a couple of years ago: Is Euler characteristic of a simplicial complex upper bounded by a ...
- 197
23
votes
6
answers
2k
views
Is there a topological description of combinatorial Euler characteristic?
There are a collection of definitions of "combinatorial Euler characteristic", which is different from the "homotopy Euler characteristic". I will describe a few of them and give some references, and ...
- 54.6k