# Tagged Questions

178 views

### What's the name of this quantity?

For each permutation $\sigma$ of $\left\{ 1, 2, \dots, n \right\}$ define $$\operatorname{dist}(\sigma)=\sum_{i=1}^{n}\left| \sigma (i)-i \right|$$ For each $n\in\mathbb{N}$, I'm interested in ...
46 views

### The name of certain permutations.

The permutations I'm looking at are 2341, 2413, 3412, 3421, 4123 and 4312. I'll explain the property with the example 2413: I start with the first digit (2) and go to the position 2. There I see the ...
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### What is the professional term for the combination of the selection in n out of the total m elements?

I know the number of combinations is called ${}_nC_r$, but what about all the exact outcomes? For example: I have $3$ elements $a,b,c$ and for the parameter $2$, I will have outcomes ab,\quad ...
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### Permutations and terminology (“subpermutations”?)

I will start with example. I have two permutations (of 5 elements) - (1 2) and (1 2)(3 5 4). When the first permutation changes something, the second do the same change (but it can do anything with ...
46 views

### Terminology: is there a term for one order being on a geodesic between two others in the Cayley graph?

Think about the graph whose nodes are total orders on a finite set, and whose edges connect orders that only differ on two elements. This is actually a Cayley graph of $S_n$, but I don't want to fix ...
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### When a Permutation is not a cycle

$\sigma = \pmatrix{1&2&3&4&5&6&7&8\\3 &8 &6 &7 &4 & 1 & 5 & 2} = (136)(28)(475)$ I just have a question about terminology. Would it be correct ...
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### Orbit vs. Cycle

Can someone explain to me the difference between an orbit and a cycle?