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Results tagged with co.combinatorics
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user 34435
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
2
votes
Which unordered partition of $n$ gives rise to the largest number of ordered partitions?
Some heuristic way to the answer, related to well-known properties of the entropy of probability distributions, is loosely as follows.
Set $m=\sum_i a_i$ and $p_i=a_i/m$, so that $p=(p_i)_{i\ge1}$ is …
- 456
9
votes
The probability for a streak when tossing a coin
The survey: ENUMERATION OF STRINGS by A. M. Odlyzko, available at
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.76.5995&rep=rep1&type=pdf
gives an answer for a fair coin, I think, for it …
- 456
3
votes
Overlapping sets
In Research Problems in Discrete Geometry by Peter Brass, William O. J. Moser, János Pach, in section 2.1 page 75, "Decomposition of multiple packings and coverings", problems with a similar flavour a …
- 456
5
votes
Accepted
Counting graphs up to isomorphism
For question 1, I believe you refer to unordered trees, for which a summary of the available information is given page 4 of "The CRT is the scaling limit of unordered binary trees" by Marckert and Mie …
- 456
5
votes
Accepted
Analogy between Integers and Permutations
The essential common feature that insures convergence to a Poisson Dirichlet distribution is explained in the book "Logarithmic Combinatorial Structures" by Arratia Barbour and Tavare. They do a great …
- 456
1
vote
Analogy between Integers and Permutations
If I remember well, there is also a correspondence between the degrees of factors of polynomials in $\mathbb{F}_q[X]$, the size of cycles of riffle-shuffle permutations (a brand of non-uniform random …
- 456