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Results tagged with co.combinatorics
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user 35416
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
47
votes
Accepted
Roots of permutations
$\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\SL}{SL}$
The maximum of the function counting square roots is attained at $x_0=1$ and this statement generalises quite well.
Let $s(\chi)$ denote …
- 13k
13
votes
Branching rule from symmetric group $S_{2n}$ to hyperoctahedral group $H_n$
This is an answer to the second question: I ran an experiment with $S_6$ (which was the best guess due to the famous "oddness" of 6). There are two subgroups in $S_6$ isomorphic to this involution cen …
- 13k
11
votes
A sum involving derivatives of Vandermonde
Here is a direct way to obtain Denis Serre's formula:
Just note that $x_i^k\frac{\partial^k}{\partial x_i^k}$ multiplies a monomial in the determinant by $\frac{r!}{(r-k)!}$ where $r$ is the power of …
- 13k