Abstract Algebra. How to multiply permutations in cycle notation

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Title: Abstract Algebra. How to multiply permutations in cycle notation
Abstract: I explain how to multiply permutations using cycle notation.
This video accompanies pages 32-37 of the class notes (www.math.colostate.edu/~adams...) for an "Introduction to Abstract Algebra" class (www.math.colostate.edu/~adams...)

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25 мар 2020

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Комментарии : 64

@sinja_believer 12 дней назад

Thanks for giving us the best explanation.

@johanlouisgouws3628 Год назад

Absolute GOAT in maths. Thank you so much

@HenryAdamsMath Год назад

Happy to help!

@riyakeerthana3136 8 дней назад

Thank u for ur crystal clear explanation

@sangavi2305 8 месяцев назад

Competent teacher👏👏👏well explainer👍

@HenryAdamsMath 8 месяцев назад

Thank you! 😃

@user-wc1mb2ql9x 2 года назад

Love you professor!!

@MasiKarimi 2 месяца назад

Thanks a lot for the info! Awesome teaching!

@HenryAdamsMath 2 месяца назад

You are welcome!

@georg.gamsbichler Месяц назад

Very well done!

@HenryAdamsMath 25 дней назад

Thank you very much!

@AlexD-wd6jx 4 месяца назад

Great explanation, much appreciated!

@HenryAdamsMath 2 месяца назад

Glad it was helpful!

@wenyaoma260 2 года назад

It is very helpful! Thanks to your video!

@HenryAdamsMath 2 года назад

Great, I'm glad it was helpful!

@07.not.out.msd. Год назад

Great work man!🔥

@HenryAdamsMath Год назад

Thanks!

@abigailhall51 2 года назад

this was such a great explanation thanks loads from Manchester :)

@HenryAdamsMath 2 года назад

Wonderful, thanks, you bet!

@samiaurin2354 Год назад

Thank you so much! It helped me a lot to do my homework.

@HenryAdamsMath Год назад

You're welcome!

@user-qs1tp1ll9i Год назад

Awesome explanation!

@HenryAdamsMath Год назад

Thank you!

@yourali1568 Год назад

Thank you form kuwait ❤️❤️

@HenryAdamsMath Год назад

You are welcome!

@teachercomment801 Год назад

Thank you so much sir!

@HenryAdamsMath Год назад

You bet!

@kassembardan1601 Год назад

Very good method Bravoo many thx

@HenryAdamsMath Год назад

Thank you!

@ezrakim1323 Год назад

This is sooo amazing🔥🔥🔥

@HenryAdamsMath Год назад

Thanks!

@miyamotomusashi4556 5 месяцев назад

Thanks a lot!

@HenryAdamsMath 5 месяцев назад

You're welcome!

@stanleeleo9019 2 года назад

Thank you !

@HenryAdamsMath 2 года назад

You're welcome!

@azizyosri2058 2 года назад

thank you so much !

@HenryAdamsMath 2 года назад

You are welcome!

@alamdarshah8595 11 месяцев назад

helped alot .... thank you...

@HenryAdamsMath 10 месяцев назад

You are welcome!

@naveenkumar-wo5yx 3 года назад

Very nice explanation

@HenryAdamsMath 3 года назад

Thank you!

@hydose1 5 месяцев назад

@10:28 actually 3 goes back to 1 based on the left cycle.

@BairdBanko 3 года назад

Permutations are awesome!

@HenryAdamsMath 3 года назад

I agree!

@sehrish3444 2 года назад

Great explanation ❤️😍

@HenryAdamsMath 2 года назад

Glad you think so!

@Bagunka 3 года назад

Great video as always! Also now you look younger than a year ago!

@HenryAdamsMath 3 года назад

Haha, thank you!

@subhadipsarkar7692 2 года назад

Thank you❤️

@HenryAdamsMath 2 года назад

Certainly, you bet!

@lordnk3698 2 года назад

thank you very much

@HenryAdamsMath 2 года назад

Glad it helped!

@n1773r 2 года назад

These look so fun to solve. Great explanation btw! You saved me because my notes are horrible.

@HenryAdamsMath 2 года назад

Happy to help!

@gustavocortico1681 2 года назад

Is there a way to find "canonical" permutations? That is, the minimum number of functions that can be composed to give all the possible permutations on a finite set?

@HenryAdamsMath 2 года назад

Great question! I would refer you to the table on the second page of Keith Conrad's notes kconrad.math.uconn.edu/blurbs/grouptheory/genset.pdf. You can generate S_n with all transpositions, which is a set of size (n choose 2). But that is overkill. Alternatively, you can get away with only n-1 well-chosen transpositions. But that is again overkill. It turns out that the transposition (1,2) and the n-cycle (1,2,3,...,n-1,n) suffice to generate S_n (for all n >= 3) ! Those notes also describe some other ways to generate S_n with only two elements. You may also be interested in the following links: mathoverflow.net/questions/24101/natural-generating-sets-for-symmetric-groups www.mathcounterexamples.net/generating-the-symmetric-group-with-a-transposition-and-a-maximal-length-cycle/ www.jstor.org/stable/2974644

@gustavocortico1681 2 года назад

Thank you very much for the content! I will read this

@Alexander-tw2kw 6 месяцев назад

Thanks a lot for the explanation. If we're given a permutation, how do we find all permuations that commute with it?

@HenryAdamsMath 6 месяцев назад

You may be interested in the page math.stackexchange.com/questions/4296033/all-permutations-that-commute-with-a-cycle

@Alexander-tw2kw 6 месяцев назад

@@HenryAdamsMath thank you!

@vadiquemyself 9 месяцев назад

but why do you compose them right-to-left? I do it so : (1 2) + (2 3) = (1 2 3) and not the inverse (3 2 1) as it would be for (2 3) + (1 2) = (3 2) + (2 1) or don't u 🤔 ..... your example looks particularly commutative (1 4 3 2) + (1 3) + (2 4) also sums to (1 2 3 4) when (1 4 3 2) is done first

@HenryAdamsMath 8 месяцев назад

I am also composing right to left, so the permutation on the right acts first!