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Results tagged with co.combinatorics
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user 56553
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
5
votes
2
answers
277
views
Number of Dyck paths with prescribed number of edges
I am trying to find a formula for the trace of certain matrix. To do that I was forced to determine the number of Dyck paths with prescribed number of edges.
By a Dyck path I mean a lattice path from …
- 2,188
9
votes
3
answers
404
views
An explicit representation for polynomials generated by a power of $x/\sin(x)$
The coefficients $d_{k}(n)$ given by the power series
$$\left(\frac{x}{\sin x}\right)^{n}=\sum_{k=0}^{\infty}d_{k}(n)\frac{x^{2k}}{(2k)!}$$
are polynomials in $n$ of degree $k$. First few examples:
$ …
- 2,188