베티 수

노트

위키데이터

• ID : Q429593

말뭉치

1. In algebraic topology, a mathematical discipline, the Betti numbers can be used to distinguish topological spaces.
2. Intuitively, the first Betti number of a space counts the maximum number of cuts that can be made without dividing the space into two pieces.
3. The term "Betti numbers" was coined by Henri Poincaré after Enrico Betti.
4. Poincaré proved that Betti numbers are invariants and used them to extend Euler's polyhedral formula to higher dimensional spaces.
5. Given a topological space , the Betti number of , denoted , is a nonnegative integer defined in any of the following equivalent ways.
6. In topology, Betti numbers represent the various dimensions of a topological space in regards to the number of holes that are present.
7. How is a Graph's Betti Number Related to its Genus?.
8. In this article, we compute all the Betti numbers of J G in terms of the Betti numbers of J H and as a consequence, we get the Betti diagram of wheel graph.
9. and the number of extremal Betti numbers of S / I(G) is equal to b will be constructed.
10. …a list of numbers, called Betti numbers in honour of the Italian mathematician Enrico Betti, who had taken the first steps of this kind to extend Riemann’s work.
11. Informally, the kth Betti number refers to the number of k-dimensional holes on a topological surface.
12. The Poincaré polynomial of a surface is defined to be the generating function of its Betti numbers.
13. The first Betti number b 1 (G) equals |E|+|C|-|V|.
14. There is an alternate reading, namely that the Betti numbers give the dimensions of spaces of harmonic forms.
15. Informally, the Betti number is the maximum number of cuts that can be made without dividing a surface into two separate pieces (Gardner 1984, pp. 9-10).
16. The Betti numbers are uniquely determined by requiring that be the minimal number of generators of for all .