MATH 111 m4

MATH 111 m4 - MODEL ANSWERS TO THE FOURTH HOMEWORK 2....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MODEL ANSWERS TO THE FOURTH HOMEWORK 2. Chapter 3, Section 1: 1 (a) 1 2 3 4 5 6 4 5 2 1 3 6 . (b) 1 2 3 4 5 3 1 2 4 5 . (c) 1 2 3 4 5 1 4 3 2 5 . 5. It suffices to find the cycle type and take the lowest common multi- ples of the individual lengths of a cycle decomposition. (a) (1 , 4)(2 , 5 , 3) Order 6. (b) (1 , 3 , 2) Order 3. (c) (2 , 4) Order 2. 2. Chapter 3, Section 2: 1 As and are cycles, we may find integers a 1 , a 2 , . . . , a k and b 1 , b 2 , . . . , b l such that = ( a 1 , a 2 , . . . , a k ) and = ( b 1 , b 2 , . . . , b l ). To say that and are disjoint cycles is equivalent to saying that the two sets S = { a 1 , a 2 , . . . , a k } and T = { b 1 , b 2 , . . . , b l } are disjoint. We want to prove that = . As both sides of this equation are permutations of the first n natural numbers, it suffices to show that they have the same effect on any integer 1 j n ....
View Full Document

Page1 / 3

MATH 111 m4 - MODEL ANSWERS TO THE FOURTH HOMEWORK 2....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online