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Results tagged with co.combinatorics
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user 128502
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
4
votes
0
answers
134
views
Is a group determined by the number of ways its elements multiply to the identity under some...
Let $G$ be a group, and for each ordered $n$ tuple $(g_1,...g_n)$ of elements of $G$, consider the function $f_n$ that outputs the number of permutations $\sigma\in S_n$ for which $g_{\sigma(1)}g_{\si …
- 1,949
1
vote
0
answers
97
views
Do you recognise this setup of structure on a poset?
The setup is that we have a finite poset $P$, with a multiplicative rank function $r_{xy}:P\times P\rightarrow \mathbb{N}$, and a symmetric pairing $\langle\ ,\ \rangle:P\times P\rightarrow\mathbb{N}$ …
- 1,949
3
votes
Accepted
The sum of the signs of conjugacy classes in the symmetric group S_n
We'll can prove this with Clifford theory and some counting, for the normal subgroup of $A_n$ in $S_n$. Let $\tau$ be a transposition in $S_n$.
Splitting into simple lemmas:
$r$ is the number of orbi …
- 1,949