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visits member for 2 years, 9 months
seen Nov 23 at 17:04

Computer engineer: a lot of C, PHP, and Python, plus a bit of lots of other stuff. Linux user. Amateur cryptonerd and general science and math geek.


Sep
24
awarded  Autobiographer
Jul
2
awarded  Curious
Jun
11
accepted How to denote domain and range
Jun
11
asked How to denote domain and range
Mar
18
accepted Enumerating cases for conditional probability
Mar
1
accepted Understanding group presentation as a quotient
Mar
1
comment Understanding group presentation as a quotient
Wow, nice answer, thanks for putting in the time! I'm going to have to put in some time studying it some more to understand it, but I think I was able to follow each step, just haven't quite pulled it all together into a conclusion yet. Also, I think there's a typo in the last paragraph: you have $fef$ listed twice in $\hat{G}$.
Feb
28
asked Understanding group presentation as a quotient
Feb
26
accepted Show that group action is homomorphism to Symmetric group
Feb
26
comment Show that group action is homomorphism to Symmetric group
Oh, ok. So my original formulation for the condition of homomorphism was off. I think it makes sense now, thanks!
Feb
26
comment Show that group action is homomorphism to Symmetric group
Actually, I take that back, $A_g(x)$ is not a permutation of $X$, it's an element of $X$. So how can you compose a permutation/function, $A_g$ with an element of a set, $A_f(x)$?
Feb
26
comment Show that group action is homomorphism to Symmetric group
@SpamIAm: Thanks, but I think you over estimate me. I have the axioms written out as $A(e,x) = x$ for all $x$ (where $e$ is the identity of $G$) and $A(g, A(f,x)) = A(g+f, x)$, but it's still not clear to me why this defined a homomorphism.
Feb
26
comment Show that group action is homomorphism to Symmetric group
(Thanks for updating from $h$ to $A$). So the steps to change right side, $A(g+f,x)$ into $A_g * A_f(x)$ are clear, but is that necessarily equal to $A_g(x) * A_f(x)$. I know $A_g(x)$ and $A_g$ are both permutations of X, but are they they same?
Feb
26
comment Show that group action is homomorphism to Symmetric group
@ThomasAndrews: Thanks, I've updated the question to use $A$ in place of $h$: I'm not sure why I started using $h$, must be misread something somewhere. So if $A$ is the group action, we have $A : G \times X \to X$, to it $A$ takes a two-tuple $(g,x)$ with $g \in G$ and $x \in X$.
Feb
26
revised Show that group action is homomorphism to Symmetric group
edited body
Feb
26
asked Show that group action is homomorphism to Symmetric group
Feb
24
accepted Notation for nested sigmas (summations)
Feb
21
comment Notation for nested sigmas (summations)
Oh, that's right, I forgot you can iterate over a set of tuples. But it doesn't really resolve the question of how to neatly define the set from which they draw, which is kind of the big problem in the originally posted example.
Feb
21
asked Notation for nested sigmas (summations)
Feb
19
comment Enumerating cases for conditional probability
Thanks. That's nearly what I came up with as described in the question, but it is not any more clear to me why you don't need $\binom{8}{4}$ included somewhere as this is the total number of ways in which you can choose which four bits are set and which four are cleared.