Exercise 8.4. Suppose o e Sym(n) is a k-cycle. Show that TOT-¹ is also a k-cycle for every 7 € Sym(n). More precisely, show that if o = (a₁a2... ak), then TOT 1 = (T(α₁) T(a₂)... T(ak)).
Exercise 8.4. Suppose o e Sym(n) is a k-cycle. Show that TOT-¹ is also a k-cycle for every 7 € Sym(n). More precisely, show that if o = (a₁a2... ak), then TOT 1 = (T(α₁) T(a₂)... T(ak)).
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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Transcribed Image Text:Exercise 8.4. Suppose σ € Sym(n) is a k-cycle. Show that TOT-¹ is also a k-cycle for
every 7 € Sym(n).
More precisely, show that if o = (a₁ a2 ... ak), then TOT−¹ = (T(A₁) T (A2) ….. 7(ak)).
1
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