Am I right that conjugacy classes of group $A_n$ can be obtained from conjugacy classes of $S_n$ (which are in correspondence with Young diagrams). If class $$C(h)=\{\sigma h {\sigma}^{-1}|\sigma\in S_n\}$$ contains independent cycles of only odd length and length of all cycles are different then $C(h)$ in $A_n$ split to two classes $$C_1(h)=\{\sigma h {\sigma}^{-1}|\sigma\in A_n\}$$ $$C_2(h)=\{\sigma \tau h {\tau}^{-1} {\sigma}^{-1}|\sigma\in A_n\}.$$ I only interested in the answer.  Thanks a lot!
Browsing  I came across this:  The conjugacy class of an element $g\in A_{n}$:  splits if the cycle decomposition of $g\in A_{n}$ comprises cycles of distinct odd length. Note that the fixed points are here treated as cycles of length $1$, so it cannot have more than one fixed point; and does not split if the cycle decomposition of $g$ contains an even cycle or contains two cycles of the same length.   Anybody with a proof?
bash profile works for user but not sudo What editors/IDEs are available for easing the process of writing TeX/LaTeX documents? Please state some useful features like code completion, spell checking, building final DVI or PDF files, etc.  This question is undergoing a systematic refurbishment, see  on Meta. If you’d like to see another editor feature covered here or to take care of an editor that’s not covered yet, share your ideas in that meta question.  List of editors Links to answers. How does chain fishing work? I am a novice user and I am trying to install Oracle Java. The process calls for me to access /usr/local/java, but here is the problem. I get as far as /usr/local, then this is the message I get:  leonard@leonard-MT6452:/usr/local$ dir bin  etc  games  include  java  lib  man  sbin  share  src  leonard@leonard-MT6452:/usr/local$ cd /java/ bash: cd: /java/: No such file or directory  leonard@leonard-MT6452:/usr/local$ rm -r ~/java rm: cannot remove ‘/home/leonard/java’: No such file or directory   Help? I'm trying to prove by induction that for all $a,b \in \mathbb{Z}$ and $n \in \mathbb{N}$, that $(a-b) \mid (a^n-b^n)$. The base case was trivial, so I started by assuming that $(a-b) \mid (a^n-b^n)$. But I found that: \begin{align*} (a-b)(a^{n-1}+a^{n-2}b + a^{n-3}b^2+...+b^{n-1}) &amp;= a^n-b^n. \end{align*}  Doesn't this imply that $(a-b) \mid (a^n-b^n)$ as $a^{n-1}+a^{n-2}b+\dots+b^{n-1}$ is clearly an integer? This obviously isn't a proof by induction, but is there anything wrong with taking this approach to prove this result, other than the fact that it isn't what is being asked?   Aside, I'm having trouble getting started with the proof by induction. I've tried making the above equivalence useful during the induction step, but it doesn't seem to be helpful, so any hints would be greatly appreciated! Empty signature file after i.gensig in GRASS I'm trying to make a supervised classification in Grass 6.4.3 under Linuxmint 16.  After digitizing the training areas, I transformed them from vector to raster. Then I've done the following: just in case: g.region rast=train_area_2013_03_05_raster@PERMANENT,2013_03_05_toar4@PERMANENT  then  i.group group=group subgroup=sub_group input=2013_03_05_toar4@PERMANENT,2013_03_05_toar5@PERMANENT,2013_03_05_toar3@PERMANENT  and   i.gensig trainingmap=train_area_2013_03_05_raster@PERMANENT group=group@PERMANENT subgroup=sub_group signaturefile=superv_class  but the resulting signature file, only contains one character: "#".  The output of i.gensig in the console is the following:  Finding training classes... 3 classes found Calculating class means... Calculating class covariance matrices... Signature 1 not invertible Signature 2 not invertible Signature 3 not invertible i.gensig complete.   Obviously if I try: i.maxlik group=group@PERMANENT subgroup=sub_group sigfile=superv_class class=results_class  I obtain the following error message:  ERROR: Unable to read signature file &lt;superv_class&gt;   I've been searching, but I couldn't find the solution.   I've tried: this   My problem is similar to this: . But here, there's no solution suggested. As in this case, I also used i.cluster to generate an unsupervised signature file and i.maxlik reads this perfectly well.   there's another similar question, but again, with no solution...  What does Signature X not invertible means?  Any idea? Thanks for your help! How can I search tags on StackOverflow Careers? I am attempting to search jobs by tag on StackOverflow Careers. On SO, this is done using square brackets, but that is simply doing a keyword search, and I still get results that don't have the tag I am looking for.  For example, when I search for the keyword "android", I get this:        which is the same as when I search for the keyword "[android]":        Is there a format I can use to search jobs by tag? If not, I believe this would be a nice feature (seems intuitive for the Stack Exchange invite-only job site). Shows "unable to locate package unzip" error I have installed Ubuntu 12.04 server , shows    E:unable to locate the package unzip   the above error is also shown, if I try to install packages also. Can any one help me out to get out from this error. Student missing exam for “medical reasons” How to add video to iphone simulator Can I manually put an external hard disk to sleep? Pay real money to set bounties (another method, not replacing rep method) It may seem like a stupid thing, but could we please be able to pay real money to set a bounty.  For example, if I had only 1 rep, I want to be able have a bounty.   Here late the suggested prices in USD. Convert money    $0.49 for each 50 reputation $0.99 for each week $1.99 for a month $9.99 for a year   Every month, the bounty fee would come in. This would mean you would have to enable your account with a bounty fee button on your profile. Update (March, 2012): This has been rolled out to all sites in the network.    Behind the scenes we've been hard at work making some changes to how we track reputation.  Here are some of the issues we're aiming to address with these changes:   Reputation Skew (your actual reputation doesn't match what's shown) Up/Down votes oddities (mostly with the daily rep cap, the magical +2) Historical Deletes (not impacting rep immediately, contributing to skew) Unaccepts (display issues in the profile) User Deletion (magically missing rep, another skew contributor)   To be clear: reputation values are not changing, every action in the system is still worth the same amount.   Here’s what will be different:   Your reputation will be correct at all times Deletions will have a much more immediate effect on reputation, not waiting on a recalc  (but reputation sync takes up to 5 minutes on a delete/undelete action; as to not block the user's response thread, it's offloaded to a background queue) Recalcs will no longer be necessary Up/Down vote reversals will restore the correct reputation amount Up/Down vote reversals will correctly adjust to the reputation cap The reputation history in your profile will be more detailed and accurate (e.g. when a post is deleted, you'll see that in the reputation tab of your profile)   This means your reputation will go up and down more than it has previously, but it will be in sync.  To think of it more easily: imagine that a recalc will be done after every action in the system.  Probably the biggest impact many will be concerned with is that you may see your reputation drop in cases where it didn't seem like it did before  This was effectively happening before, but the results of that change were not applied immediately, but on the next rep recalc.  Post deletion is the biggest factor here, previously it didn't (immediately) account for the reputation impact...that will no longer be the case.  Reputation changes from the deletion will now be applied within the hour, and most other changes will be instant.  Now the part that will make everyone throw vegetables our way:  this will require a global recalc to get everything in sync.  We'll be rolling it out first here on meta, then the rest of the network...the enabling of the detailed rep view and global recalc on each individual site will coincide.  During the rollout you will see empty reputation tabs on profiles as we transition to the new storage behind the scenes, they'll be restored as the recalc rolls though each user.  We’ll put up a blog post on  before the network-wide rollout.  If you have any questions about this change or details I may have left out, please do so in answers below so that we can clear up as much as possible before this rolls out. How to extrude and scale with an even offset? Regular expression to match DNS hostname or IP Address? MacBook [Pro] - how many displays, what resolution/frequency? How do I find out the number, type, resolution &amp; refresh rate of additional monitors I can attach to my MacBook or MacBook Pro?  This is an attempt at a canonical QA, as per the Meta QA -   to try prevent the myriad "same but different" questions we get on every possible combination of computers, cable &amp; monitors There are perfectly good resources out there that Ask Different should not have to duplicate the efforts of. How to add a program as a startup application from a terminal? I am using Ubuntu 12.04 and I know the GUI way to maintain the startup program list but now I want to find out the way to add/remove startup applications using a command line interface (CLI). Is there a way to select the children of a parent object? Can the Universe be deterministic and still allow free will? Possible Duplicate:             As asked in the title, can a Universe which is deterministic at its fundamental level still allow free will? Three side-by-side tables I am using this LaTeX code to generate three tables side by side. However, it showing errors and not giving satisfactory result. Can anyone please help me to short out the problem.  \begin{table} \centering \makebox[0pt][c]{\parbox{1.2\textwidth}{% \begin{minipage}[b]{0.265\hsize}\centering \begin{tabular}{ | c | c |c | } \multicolumn{3}{c} \hline {$q=1/10$} \\ \hline T &amp; $r_h$ &amp; $\omega$ \\  \hline 0.233 &amp; 0.135 &amp; 2.38486-0.34667I  \\  0.256 &amp; 0.140 &amp; 2.38092-0.35837I \\ 0.273 &amp; 0.145 &amp; 2.38049-0.35982I \\  0.278 &amp; 0.146 &amp; 2.38007-0.36130I \\  0.281 &amp; 0.147 &amp; 2.37964-0.36282I \\  \hline 0.284 &amp; 0.761 &amp; 2.54150-2.03209I \\ 0.285 &amp; 0.765 &amp; 2.54515-2.04292I \\ 0.289 &amp; 0.800 &amp; 2.57799-2.13761I \\ 0.302 &amp; 0.900 &amp; 2.67987-2.40712I \\ 0.312 &amp; 1.000 &amp; 2.79214-2.67552I \\ \hline \end{tabular} \end{minipage} \hfill \begin{minipage}[b]{0.265\hsize}\centering \begin{tabular}{ | c | c | c | } \multicolumn{3}{c} \hline {$q=1/9$} \\ \hline T &amp; $r_h$ &amp; $\omega$ \\ \hline 0.227 &amp; 0.150 &amp; 2.34385-0.41094I  \\  0.245 &amp; 0.155 &amp; 2.34215-0.41723I \\ 0.260 &amp; 0.160 &amp; 2.34056-0.42416I \\  0.271 &amp; 0.165 &amp; 2.33908-0.43175I \\  0.276 &amp; 0.167 &amp; 2.33852-0.43497I \\  \hline 0.280 &amp; 0.720 &amp; 2.50248-1.92299I \\ 0.283 &amp; 0.750 &amp; 2.52893-2.00424I \\ 0.286 &amp; 0.780 &amp; 2.55660-2.08533I \\ 0.289 &amp; 0.800 &amp; 2.57568-2.13931I \\ 0.302 &amp; 0.900 &amp; 2.67807-2.40842I \\ \hline \end{tabular} \end{minipage} \hfill \begin{minipage}[b]{0.265\hsize}\centering \begin{tabular}{ | c | c | c |} \multicolumn{3}{c} \hline {$q=1/8$} \\ \hline T &amp; $r_h$ &amp; $\omega$ \\  \hline 0.246 &amp; 0.180 &amp; 2.29733-0.50611I  \\  0.255 &amp; 0.185 &amp; 2.29654-0.51364I \\ 0.263 &amp; 0.190 &amp; 2.29589-0.52172I \\  0.269 &amp; 0.195 &amp; 2.29534-0.53033I \\  0.273 &amp; 0.199 &amp; 2.29496-0.53758I \\  \hline 0.275 &amp; 0.675 &amp; 2.46067-1.80426I \\ 0.277 &amp; 0.700 &amp; 2.48131-1.87194I \\ 0.288 &amp; 0.800 &amp; 2.57245-2.14170I \\ 0.302 &amp; 0.900 &amp; 2.67555-2.41027I \\ 0.317 &amp; 1.000 &amp; 2.78870-2.67796I \\ \hline \end{tabular} \end{minipage}% }} \end{table}