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Results tagged with co.combinatorics
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user 3920
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
9
votes
1
answer
1k
views
Vertex connectivity of random graphs?
Consider simple, undirected Erdős–Rényi graphs $G(n,p)$, where $n$ is the number of vertices and $p$ is the probability for each pair of vertices to form an edge. Many properties of these graphs are k …
- 1,354
15
votes
Sum of 'the first k' binomial coefficients for fixed $N$
Each binomial coefficient satisfies
$$\left(\frac{N}{i}\right)^i \leq {N \choose i} < \left(\frac{eN}{i}\right)^i,$$
so if $k \leq N/2$, you can upper bound the sum by $k(\frac{eN}{k})^k$
- 123