Permutations: Writing a Permutation as a Product of Disjoint Cycles

[@vector8310]

Your observation that we're trying to "get rid of redundancy" actually provides ample motivation for students with an applications bent. I'm an advocate of pure math, yet even I was appreciated the insight. New subscriber here. Thank you.

[@AdamGlesser]

@@vector8310 Very nice of you to notice. Most of my students are not pure math majors, so I'm always trying to reach across the aisle.

[@alla6631]

Sir, you are the best! Your students are very lucky! Our Professor doesn't explain anything, but expected to know everything!

[@AdamGlesser]

Glad I could help :)

[@mc811mc]

I usually don't write comments but sir, you've literally saved my life

[@AdamGlesser]

Always happy to have saved a life :)

[@rubhasreekrishnan4660]

Thank u so much.....i have searched so many videos..but you explained the best

[@agathakafuko2379]

Thankyou so much this was so amazing can't believe I understood in 5 minutes 🥺❤️

[@baroncandy3939]

I have my semester tomorrow and I was utterly confused in this I can do a bit thanks to this vid

[@lethabompotoane2820]

Thank you so much! I spent the whole day doing this😂😂😂😂... only to get it in 5 minutes

[@shawnmofid7131]

Thanks. It was just what I needed to understand it. What is the spelling of the notation name please? It sounds like you say "kochi's" notation?

[@AdamGlesser]

Cauchy

[@3lk0sak0]

Wow, only one video, which could resolve my problem. Thank You.

[@KermitTheHermit.]

Thanks for the infor sir! Was stuck quite a bit

[@kennethben-boulo7127]

Hello Is it possible to express (1 2 3 4) in S4 as a product of disjoint cycles ? Thanks

[@AdamGlesser]

Yes, but you may not like the answer. Because (1 2 3 4) is already a cycle with no repetitions, we consider it a product of disjoint cycles. I suspect you really want to know if we can write (1 2 3 4) as a product of two (or more) disjoint cycles. The answer to that is no. This is because, up to reordering the disjoint cycles, we can write any permutation as a product of disjoint cycles in only one way. Since (1 2 3 4) is already one such way, there are no others.

[@kennethben-boulo7127]

@@AdamGlesser I get it now, thank you so so much ❤️🔥🔥 Subscribed 🙂

[@nadeembhatt4058]

Thanks 👍👍👍

[@umarplayzhd5220]

Thank you!

[@mathbeyondbasics]

Thank you sir

[@drummerjuans]

Thank You! This video is much appreciated...

[@lemyul]

thank you for sharing Ada

[@firewingsipl]

sir one doubt in ans a there is only one cycle we got so this is the disjoint cycle right

[@AdamGlesser]

That's right. In order to make the language easier, we allow for "product of disjoint cycles" to include there being a single cycle. In fact, we even allow it to mean zero cycles. For example (1 2)(1 2) equals the identity permutation which, if forced do so, we would refer to as the empty product of disjoint cycles.

[@TheWolfXCIX]

Thank you very much

[@Clairesuismoimaispas]

the best video of the kind!!

[@NitinPanwar-jg5wc]

That really did help..✨✨tysm dude😎

[@AdamGlesser]

Glad to hear it. Good luck with your studies!

[@josejavierminanoramos2185]

You saved my life

[@James-zs3vm]

Thanks George Lucas