Write a permutation as a product of transpositions. [duplicate]
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How to write permutations as product of disjoint cycles and transpositions
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Let $alpha = (1 6 3) (2 9) (4 8 10) in S_{10}$ be a permutation. Write $alpha$ as a product of transpositions, i.e. of cyclic permutations of order 2. Note that transpositions do not need to be disjunked.
Really don't know how to "go/walk" on this.
I think that $$1->6, 6->3$$
$$2->9$$ $$5->8, 7->10$$
So something like $$(1 6)(6 3)(3 2)(2 9)(9 4)(4 8)(8 10)$$
permutations
asked Nov 25 at 16:32
soetirl13
114
marked as duplicate by gt6989b, Matt Samuel, Lord Shark the Unknown, user10354138, Brahadeesh Nov 26 at 8:24
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
up vote
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down vote
favorite
This question already has an answer here:
How to write permutations as product of disjoint cycles and transpositions
1 answer
Let $alpha = (1 6 3) (2 9) (4 8 10) in S_{10}$ be a permutation. Write $alpha$ as a product of transpositions, i.e. of cyclic permutations of order 2. Note that transpositions do not need to be disjunked.
Really don't know how to "go/walk" on this.
I think that $$1->6, 6->3$$
$$2->9$$ $$5->8, 7->10$$
So something like $$(1 6)(6 3)(3 2)(2 9)(9 4)(4 8)(8 10)$$
permutations
asked Nov 25 at 16:32
soetirl13
114
marked as duplicate by gt6989b, Matt Samuel, Lord Shark the Unknown, user10354138, Brahadeesh Nov 26 at 8:24
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
Can you write $(163)$ as a product of transpositions?
– gt6989b
Nov 25 at 16:36
add a comment |
up vote
0
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favorite
up vote
0
down vote
favorite
This question already has an answer here:
How to write permutations as product of disjoint cycles and transpositions
1 answer
Let $alpha = (1 6 3) (2 9) (4 8 10) in S_{10}$ be a permutation. Write $alpha$ as a product of transpositions, i.e. of cyclic permutations of order 2. Note that transpositions do not need to be disjunked.
Really don't know how to "go/walk" on this.
I think that $$1->6, 6->3$$
$$2->9$$ $$5->8, 7->10$$
So something like $$(1 6)(6 3)(3 2)(2 9)(9 4)(4 8)(8 10)$$
permutations
asked Nov 25 at 16:32
soetirl13
114
This question already has an answer here:
How to write permutations as product of disjoint cycles and transpositions
1 answer
Let $alpha = (1 6 3) (2 9) (4 8 10) in S_{10}$ be a permutation. Write $alpha$ as a product of transpositions, i.e. of cyclic permutations of order 2. Note that transpositions do not need to be disjunked.
Really don't know how to "go/walk" on this.
I think that $$1->6, 6->3$$
$$2->9$$ $$5->8, 7->10$$
So something like $$(1 6)(6 3)(3 2)(2 9)(9 4)(4 8)(8 10)$$
This question already has an answer here:
How to write permutations as product of disjoint cycles and transpositions
1 answer
permutations
permutations
asked Nov 25 at 16:32
soetirl13
114
asked Nov 25 at 16:32
soetirl13
114
edited Nov 25 at 16:41
asked Nov 25 at 16:32
soetirl13
114
asked Nov 25 at 16:32
soetirl13
114
asked Nov 25 at 16:32
soetirl13
114
114
marked as duplicate by gt6989b, Matt Samuel, Lord Shark the Unknown, user10354138, Brahadeesh Nov 26 at 8:24
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by gt6989b, Matt Samuel, Lord Shark the Unknown, user10354138, Brahadeesh Nov 26 at 8:24
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
Can you write $(163)$ as a product of transpositions?
– gt6989b
Nov 25 at 16:36
add a comment |
Can you write $(163)$ as a product of transpositions?
– gt6989b
Nov 25 at 16:36
Can you write $(163)$ as a product of transpositions?
– gt6989b
Nov 25 at 16:36
Can you write $(163)$ as a product of transpositions?
– gt6989b
Nov 25 at 16:36
add a comment |
1 Answer
1
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Hint: $(a_1a_2dots a_n)=(a_1a_2)(a_2a_3)dots(a_{n-1}a_n)$.
answered Nov 25 at 16:52
Chris Custer
9,8793624
α=(1 6 3)(2 9)(4 8 10) with your hint we got; $alpha_1$=1, $alpha_2$=6, $alpha_3$=3, $alpha_4$=2, $alpha_5$=9, $alpha_6$=4, $alpha_7$=8, $alpha_8$=10, or?
– soetirl13
Nov 25 at 17:01
Well, just split $(163)=(16)(63)$. I leave $(4 8 10)$ for you.
– Chris Custer
Nov 25 at 17:09
1
ahh (1 6)(6 3)(2 9)(4 8)(8 10)
– soetirl13
Nov 25 at 18:24
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Hint: $(a_1a_2dots a_n)=(a_1a_2)(a_2a_3)dots(a_{n-1}a_n)$.
answered Nov 25 at 16:52
Chris Custer
9,8793624
α=(1 6 3)(2 9)(4 8 10) with your hint we got; $alpha_1$=1, $alpha_2$=6, $alpha_3$=3, $alpha_4$=2, $alpha_5$=9, $alpha_6$=4, $alpha_7$=8, $alpha_8$=10, or?
– soetirl13
Nov 25 at 17:01
Well, just split $(163)=(16)(63)$. I leave $(4 8 10)$ for you.
– Chris Custer
Nov 25 at 17:09
1
ahh (1 6)(6 3)(2 9)(4 8)(8 10)
– soetirl13
Nov 25 at 18:24
add a comment |
up vote
1
down vote
Hint: $(a_1a_2dots a_n)=(a_1a_2)(a_2a_3)dots(a_{n-1}a_n)$.
answered Nov 25 at 16:52
Chris Custer
9,8793624
α=(1 6 3)(2 9)(4 8 10) with your hint we got; $alpha_1$=1, $alpha_2$=6, $alpha_3$=3, $alpha_4$=2, $alpha_5$=9, $alpha_6$=4, $alpha_7$=8, $alpha_8$=10, or?
– soetirl13
Nov 25 at 17:01
Well, just split $(163)=(16)(63)$. I leave $(4 8 10)$ for you.
– Chris Custer
Nov 25 at 17:09
1
ahh (1 6)(6 3)(2 9)(4 8)(8 10)
– soetirl13
Nov 25 at 18:24
add a comment |
up vote
1
down vote
up vote
1
down vote
Hint: $(a_1a_2dots a_n)=(a_1a_2)(a_2a_3)dots(a_{n-1}a_n)$.
answered Nov 25 at 16:52
Chris Custer
9,8793624
Hint: $(a_1a_2dots a_n)=(a_1a_2)(a_2a_3)dots(a_{n-1}a_n)$.
answered Nov 25 at 16:52
Chris Custer
9,8793624
answered Nov 25 at 16:52
Chris Custer
9,8793624
answered Nov 25 at 16:52
Chris Custer
9,8793624
answered Nov 25 at 16:52
Chris Custer
9,8793624
9,8793624
α=(1 6 3)(2 9)(4 8 10) with your hint we got; $alpha_1$=1, $alpha_2$=6, $alpha_3$=3, $alpha_4$=2, $alpha_5$=9, $alpha_6$=4, $alpha_7$=8, $alpha_8$=10, or?
– soetirl13
Nov 25 at 17:01
Well, just split $(163)=(16)(63)$. I leave $(4 8 10)$ for you.
– Chris Custer
Nov 25 at 17:09
1
ahh (1 6)(6 3)(2 9)(4 8)(8 10)
– soetirl13
Nov 25 at 18:24
add a comment |
α=(1 6 3)(2 9)(4 8 10) with your hint we got; $alpha_1$=1, $alpha_2$=6, $alpha_3$=3, $alpha_4$=2, $alpha_5$=9, $alpha_6$=4, $alpha_7$=8, $alpha_8$=10, or?
– soetirl13
Nov 25 at 17:01
Well, just split $(163)=(16)(63)$. I leave $(4 8 10)$ for you.
– Chris Custer
Nov 25 at 17:09
1
ahh (1 6)(6 3)(2 9)(4 8)(8 10)
– soetirl13
Nov 25 at 18:24
α=(1 6 3)(2 9)(4 8 10) with your hint we got; $alpha_1$=1, $alpha_2$=6, $alpha_3$=3, $alpha_4$=2, $alpha_5$=9, $alpha_6$=4, $alpha_7$=8, $alpha_8$=10, or?
– soetirl13
Nov 25 at 17:01
α=(1 6 3)(2 9)(4 8 10) with your hint we got; $alpha_1$=1, $alpha_2$=6, $alpha_3$=3, $alpha_4$=2, $alpha_5$=9, $alpha_6$=4, $alpha_7$=8, $alpha_8$=10, or?
– soetirl13
Nov 25 at 17:01
Well, just split $(163)=(16)(63)$. I leave $(4 8 10)$ for you.
– Chris Custer
Nov 25 at 17:09
Well, just split $(163)=(16)(63)$. I leave $(4 8 10)$ for you.
– Chris Custer
Nov 25 at 17:09
1
1
ahh (1 6)(6 3)(2 9)(4 8)(8 10)
– soetirl13
Nov 25 at 18:24
ahh (1 6)(6 3)(2 9)(4 8)(8 10)
– soetirl13
Nov 25 at 18:24
add a comment |
Can you write $(163)$ as a product of transpositions?
– gt6989b
Nov 25 at 16:36