sh1ftst0rm
Reputation
316
Top tag
Next privilege 500 Rep.
Access review queues
 Apr23 revised Constructor theory distinguishability added 8 characters in body Feb24 comment Big-O complexity of iterating over every substring @Tryss: Thanks, would you be able to explain this a little? In fact, I actually need to add a third nested loop, which iterates j/2 times, so I'm not sure how to extrapolate from your answer to a more general solution. Feb24 asked Big-O complexity of iterating over every substring Feb20 awarded Tumbleweed Feb13 asked Constructor theory distinguishability Feb7 awarded Popular Question Sep24 awarded Autobiographer Jul2 awarded Curious Jun11 accepted How to denote domain and range Jun11 asked How to denote domain and range Mar18 accepted Enumerating cases for conditional probability Mar1 accepted Understanding group presentation as a quotient Mar1 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 $\hat{G}$. Feb28 asked Understanding group presentation as a quotient Feb26 accepted Show that group action is homomorphism to Symmetric group Feb26 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! Feb26 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, $A_f(x)$? Feb26 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. Feb26 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? Feb26 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 $x \in X$.