# Tagged Questions

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### an elementary problem on wreath product groups with combinatorial flavor

Embarrassingly, I got stuck in solving the following elementary exercise. Let $G=H\wr \Gamma$ be a wreath product groups, $H,\Gamma$ are countable discrete groups, when $\xi\in\oplus_{\Gamma}H$, then ...
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### Variations of M,n,k-games

I just read about M,n,k-games and wondered if the following variation (with fixed $k$) has been studied as well and if there exists a name for it: Two players consecutively mark elements of ${\bf Z}$ ...
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### Is it possible to partition $\mathbb{N}_+$ into a *finite* family of sets completely not closed under $+$?

Let's say that $A \subseteq \mathbb{N}_+$ is completely not closed under $+$ if $$\forall_{a,b \in A}[{a+b \notin A}]$$ Is it possible to partition $\mathbb{N}_+$ into a finite family of sets ...
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### Conjugating a permutation

I am trying to see that two permutations are conjugate exactly when they have the same cycle decomposition. I fail to see that $$r(i_1,i_2,\dots,i_k)r^{−1}=(r(i_1),r(i_2),\dots,r(i_k))$$ Any thoughts ...
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### Calculation related to the number of conjugacy classes of the symmetric group

The symmetric group on $n$ elements, $S_n$, can act on itself by conjugation. The orbits of this action are the conjugacy classes corresponding to integer partitions of $n$. If $S_n$ acts on some ...