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#1 2014-12-31 02:26:42

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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Canonical Cycle Notation

I do not understand why these two are equal:
(1 2 3) = (1 2) (1 3)


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#2 2014-12-31 02:46:49

zetafunc
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Registered: 2014-05-21
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Re: Canonical Cycle Notation

Unfortunately, some people do composition on the left, and some do it on the right. In your example, you're doing composition from the left -- i.e. (1 2) is done first, then (1 3):

Applying (1 2):

1 -> 2
2 -> 1
(3 -> 3)

Then applying (1 3):

1 -> 2 -> 2 i.e. 1 -> 2
2 -> 1 -> 3 i.e. 2 -> 3
3 -> 3 -> 1 i.e. 3 -> 1

which, of course, is the same as (1 2 3).

I myself prefer composition on the right, although I can understand why many don't.

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#3 2014-12-31 02:50:36

anonimnystefy
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From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Canonical Cycle Notation

I like composition from the right as well but don't like that notation. I prefer to call that permutation (2 3 1).

Last edited by anonimnystefy (2014-12-31 02:51:15)


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#4 2014-12-31 03:37:11

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
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Re: Canonical Cycle Notation

Thanks.

Is composition not commutative?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#5 2015-01-01 04:59:01

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Canonical Cycle Notation

Try composing (12) and (13) both ways.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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