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Results tagged with co.combinatorics
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user 979
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
2
votes
Sequence of semi-standard Young tableaux, counting
For new exact formulas for these quantities, and their asymptotics, you maybe should see the recent papers
http://arxiv.org/abs/1109.1412
http://arxiv.org/abs/1208.3443 (Theorem 1.2)
and especially …
1
vote
Turning Trees into 1-dimensional curves
Yes, if the tree is rooted and planar (that is, children at each vertex are linearly ordered), you can construct its contour function. See, for example, http://www.math.ens.fr/~legall/Rio-lectures.pdf …
0
votes
can the Newton's identities and Dodgson's condensations be proved by Gessel-Viennot's lemma?
A little off-topic: Gessel-Viennot's lemma was also discovered by Karlin and McGregor (1959, "Coincidence Probabilities") and was used to construct dynamics of noncolliding systems of particles: take …
4
votes
universality of Macdonald polynomials
There is a result by Sergei Kerov (in his book Asymptotic representation theory of the symmetric group and its applications in analysis) which somewhat charaterizes the Macdonald symmetric functions. …
12
votes
4
answers
1k
views
Asymptotics of q-Catalan numbers
q-Catalan numbers are defined recurrently as C0=1, $C_{N+1}=\sum_{k=0}^N q^k C_k C_{N-k}$.
What can be said about the asymptotics of Cn when 0<q<1?
P.S. In the case q>1 it is known that as n goes to …
14
votes
5
answers
4k
views
Are there more connected or disconnected graphs on $n$ vertices?
Suppose we are talking about graphs with $n$ labeled vertices. Which graphs are more common: connected or disconnected?
3
votes
0
answers
291
views
Exchangeable or iid random variables and linear conditioning
Let $X_1,\ldots ,X_N$ be independent identically distributed random variables (or, more generally, exchangeable random variables,
but let's assume independence for simplicity). Then
$$
E(X_i\mid X_1+ …
10
votes
1
answer
260
views
q-versions of the geometric distribution and their names
I'm trying to set straight various $q$-deformations of the standard geometric distribution.
The geometric distribution on $\left\{ 0,1,\ldots \right\}$ is well-known, it has
$$
\mu_1(X=j)=(1-p)p^j,\q …