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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.
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 $k(\frac{eN}{k})^k$
- 383
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 …
- 383