4 5 1 f = 4 2 3 6 7 3 6 2 7 1 (a) Write f as a product of transpositions (not necessarily disjoint), separated by commas (e.g. (1, 2), (2, 3),... ). f = (b) Write f- as a product of transpositions in the same way. f-1 = %3D Assume multiplication of permutations f,g obeys the rule (fg)(x) = f(g(x)) so (1, 3)(1, 2) = (1,2, 3) not (1,3,2).
4 5 1 f = 4 2 3 6 7 3 6 2 7 1 (a) Write f as a product of transpositions (not necessarily disjoint), separated by commas (e.g. (1, 2), (2, 3),... ). f = (b) Write f- as a product of transpositions in the same way. f-1 = %3D Assume multiplication of permutations f,g obeys the rule (fg)(x) = f(g(x)) so (1, 3)(1, 2) = (1,2, 3) not (1,3,2).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 83E
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Let ?f be a permutation on the set {1,2,3,4,5,6,7}{1,2,3,4,5,6,7}, defined as follows
Transcribed Image Text:1 2 3 4 5
4 3 6 2
6 7
f =
7
1
5
(a) Write f as a product of transpositions (not necessarily disjoint), separated by commas (e.g. (1, 2), (2, 3), ... ).
f =
(b) Write f- as a product of transpositions in the same way.
f-1
Assume multiplication of permutations f,g obeys the rule (fg)(x) = f(g(x)) so (1, 3)(1, 2) = (1,2, 3) not (1, 3,2).
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