How many permutations of length 2n have a cycle of length n + 1? Explain your...

How many permutations of length 2n have a cycle of length n + 1?

Explain your answer.

Expert Solution

orchestra answered 2 years ago

(a)Count the number of length n permutations conisting of a single cycle, when written in cycle...

(a)Count the number of length n permutations conisting of a single cycle, when written in cycle notation. (Explain your answer.) (b)How many permutations of length 2n have a cycle of length n + 1? (Explain your answer.)

What is a gamete? A zygote? How many chromosomes do they have (n or 2n)? Are...

What is a gamete? A zygote? How many chromosomes do they have (n or 2n)? Are they haploid or diploid cells? Describe two different aspects of meiosis that contribute to genetic variation between individuals.

1a. Proof by induction: For every positive integer n, 1•3•5...(2n-1)=(2n)!/(2n•n!). Please explain what the exclamation mark...

1a. Proof by induction: For every positive integer n, 1•3•5...(2n-1)=(2n)!/(2n•n!). Please explain what the exclamation mark means. Thank you for your help! 1b. Proof by induction: For each integer n>=8, there are nonnegative integers a and b such that n=3a+5b

consider “COLLEGEOFENGINEERING” a) How many permutations are there total? b) How many permutations start and end...

consider “COLLEGEOFENGINEERING” a) How many permutations are there total? b) How many permutations start and end with vowels? c) How many permutations do NOT have consecutive vowels in them? d) How many permutations contain the vowels in order (all Es before All Is before all Os)? e) How many permutations contain the substring "GINGER"?

How many ±1-sequences of length n are there?For example, (1, −1, −1, 1) is not a...

How many ±1-sequences of length n are there?For example, (1, −1, −1, 1) is not a happy sequence, because although 1 ≥ 0 and 1 − 1 ≥ 0,the sum 1−1−1 is negative, so the condition fails for k = 3.

How many arrangements of length n where 1 ≤ n ≤ 8 can be formed from...

How many arrangements of length n where 1 ≤ n ≤ 8 can be formed from the letters A, A, B, C, C, C, D, E where (a) both A’s are adjacent? (b) the string starts or ends with A? (c) you use (exactly) 4 letters from the list?

[02] For n ≥ 1, how many strings of length n using letters a,b,c are there...

[02] For n ≥ 1, how many strings of length n using letters a,b,c are there if the letter a must occur an even number of times?

1. a. How many permutations are there of the letters {A,B,C,D,E,F}? Of there, how many are...

1. a. How many permutations are there of the letters {A,B,C,D,E,F}? Of there, how many are even? b. Express the permutation BAFEDC in P6 in cycle notation and determine whether it is even or odd. c. Determine the composition BAFEDC*BCAFDE in P6. Is the composition even or odd? d. What is the members of P6 whose cycle notation (1345)(26)?

How many permutations of the letters m, n, o, p, q contain the string mn or...

How many permutations of the letters m, n, o, p, q contain the string mn or the string mo or the string op-last year exam?

1. How many permutations of the 26 letters are there that contain none of the sequences...

1. How many permutations of the 26 letters are there that contain none of the sequences ROCK, STONE, PLUG, FIT or HAY?

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