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Results tagged with co.combinatorics
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user 81488
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
3
votes
Accepted
Probability of covering a set
Let $Z(m)$ be the number of uncovered (= not chosen) sites after $m$ trials. First, we have
$$\mathbb{E} Z(N^a(1+\epsilon)\ln N)=N\times(1-N^{-a})^{N^a(1+\epsilon)\ln N}\approx N^{-\epsilon},$$ so you …
- 1,897
0
votes
Accepted
Distribution of the cover time of a finite path?
It seems that formula (5.7) of Chapter XIV of the 1st volume of Feller may be used to obtain the full distribution of $C_n$ (as distribution of sum of two independent r.v.'s with explicit distribution …
- 1,897
7
votes
Accepted
How many times does a simple symmetric random walk of length n return to the origin?
All these questions are answered in paragraph 6 of Chapter III of Volume 1 of "An Introduction to Probability Theory and its Applications" by Feller.
In particular:
(1) $p=1/2$ is indeed the "right" …
- 1,897
5
votes
Accepted
Distribution of the area statistic for Catalan paths
Notice that the number of Catalan paths of area at least $cn^{\frac{3}{2}+\varepsilon}$ is less than the number of all paths that deviate from the horizontal axis by at least $n^{\frac{1}{2}+\varepsil …
- 1,897