Superpermutations

Factorials

1

How are factorials related to superpermutations?

Factorials can be used the number of permutations

2

5!

120

3

6! - 7!

−4320

4

What is a factorial?

The product of all positive integers from a given number down to 1.

5

(6!)(7!)

3,628,800

Permutations

1

Give an example of a permutation

Many answers

2

What are the number of permutations of 1,2,3

6

3

What are the permutations of 1,2,3

123, 132, 213, 231, 312, 321

4

What are the permutations of 1,2,3,4?

1234, 1243, 1324, 1342

2134, 2143, 2314, 2341

3124, 3142, 3214, 3241

 4123, 4132, 4213, 4231

5

What is the number of permutations for 1,2,3,4,5,6?

720

Superpermutation

1

What is a superpermutation?

A superpermutation on n symbols is a single sequence that contains every possible permutation of those n symbols as a contiguous substring.

2

How do you find the minimum length for a superpermutation (if n<6)

n! + (n-1)! + (n-2)! … (1)

3

Minimum Length of 1,2,3,4

33

4

Minimum Length of 1,2,3,4,5,6

Unknown

5

Find the minimum superpermutation length of R,G

 R,G,R or G,R,G