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A cycle (i iz is ... in) is called an n-cycle. If n 2 then the n-cycle is called transposition. Note that an n-cycle (i iz is ... in) can always be expressed as product of transpositions as follows (i, iz is ... in) = (i1 in)(in in-1)(n in-2) (i, i3)(i, i2). Write cach of the following as a product of transpositions. (a) (1 32 4) e S4. (b) (1 4 3)(2 5 6 7) e S7. (c) (143 6)(2 95 7 8) e Sy.

A cycle (i iz is ... in) is called an n-cycle. If n 2 then the n-cycle is called transposition. Note that an n-cycle (i iz is ... in) can always be expressed as product of transpositions as follows (i, iz is ... in) = (i1 in)(in in-1)(n in-2) (i, i3)(i, i2). Write cach of the following as a product of transpositions. (a) (1 32 4) e S4. (b) (1 4 3)(2 5 6 7) e S7. (c) (143 6)(2 95 7 8) e Sy.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A cycle (i iz iz .. in) is called an n-cycle. If n = 2 then the n-cycle is called a transposition. Note that an n-cycle (i iz iz ... in) can always be expressed as a product of transpositions as follows (i iz iz ... in) = (i1 in)(i1 in-1)(i1 in-2) ·*· (i1 i3)(i, iz). Write each of the following as a product of transpositions. (a) (1 32 4) E S4. (b) (1 4 3)(25 6 7) e S7. (c) (14 3 6)(2 9 5 7 8) E Sg.
Transcribed Image Text:A cycle (i iz iz .. in) is called an n-cycle. If n = 2 then the n-cycle is called a transposition. Note that an n-cycle (i iz iz ... in) can always be expressed as a product of transpositions as follows (i iz iz ... in) = (i1 in)(i1 in-1)(i1 in-2) ·*· (i1 i3)(i, iz). Write each of the following as a product of transpositions. (a) (1 32 4) E S4. (b) (1 4 3)(25 6 7) e S7. (c) (14 3 6)(2 9 5 7 8) E Sg.
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